Preventing flystrike in a rabbit?

I have had a bad past when it comes to taking care of rabbits, and I have not cared about them nearly as much as I should have, but this is a case of rabbit care that I intend to take seriously.
Early this year, I had three rabbits in total; two of them have since died. Neither rabbit died of old age (both were probably about four years old), and as at least one of them had flies landing on it not long before it died, I believe that there is a chance that both rabbits died of flystrike. It was only today that I found out that flystrike is both possible and a serious problem in rabbits (I previously believed that it was only possible in sheep). The rabbits were kept outdoors, and my remaining rabbit is currently being kept outdoors as well.
Today was a hot day, and I noticed that my remaining rabbit had some flies landing on it. I wanted to stop this from happening, so I removed most of the dung-covered fur that it had around its rear. This filthy fur had been present for at least several weeks, and I am aware that leaving it in this condition was inexcusable (I thought that the soiled fur would eventually fall off, as I have seen happen at least once before). Removing this fur, however, did not stop the problem of flies landing on my rabbit. It was after this that I looked up flystrike in rabbits and found out that it was a real possibility, and I don't want to lose my rabbit to the condition. Subsequently, I took the rabbit inside and used warm water to wash its rear (I am aware of the fact that rabbits should never be given full-body washes); warm water can apparently lure out maggots, but I saw none. This was clearly a very stressful experience for the rabbit, but it did not struggle or scream. I carefully cleaned the rabbit's behind and removed one possible maggot egg, as well as all of the remaining dirty fur. As I write this, the rabbit is drying off in a cardboard box, where it will hopefully calm down.
I am not allowed to keep the rabbit inside to prevent the possibility of flystrike. It would not like being kept inside, anyway, because it has a fairly large outdoor enclosure all to itself. I do not want to have to clean my rabbit's rear every day, because catching and cleaning it is difficult for me and very unpleasant for the rabbit. I doubt that removing a large number of the flies that live outdoors is a viable option, and I don't know about any medicine for preventing flystrike in rabbits that is available in my country.
I would appreciate any advice from experienced individuals.

Nasty, filthy fur comes from living in nasty, filthy conditions. If the rabbit is living in clean conditions, it shouldn't be able to get all gross like that. Rabbit cages with wire floors were developed to prevent this problem; the feces falls through and is removed from the ground beneath the cage on a regular basis. If your rabbit is living on solid surfaces rather than a wire floor, it is going to take a lot more work to keep it clean, but you will need to scrape out the places where the rabbit sits at least daily; providing some sort of removable, absorbent material (like wood shavings or straw) to keep the area as dry as possible will help, too.

First of all, thourghly clean your rabbits housing. As @Bunnylady said, you may want to invest in a wire cage. Next, remove all possible attractions for flies(if your manure pile is neat your rabbit, move the pile, etc). I don't think medicines will be necessary, but if the situation gets worse, you may want to contact a veterinarian. Invest in some fly spray, which you can spray at the manure to keep the flies away. DO NOT spray it at or near the rabbit. Until the flies leave, groom your rabbit(brushing, bathing it's rear if necessary) often, at least once a week. Hope the fly situation gets better!!

I have thoroughly cleaned my rabbit's hutch, and I have not seen my rabbit expressing any strange behaviour, so I don't think flystrike is something to worry about for now.
To discourage flies from proliferating, I've come up with a "strategy" that may help; every day I remove the chicken dung around my rabbit's enclosure by hosing it down so it dissolves into the soil. I'm not sure how much this will help in keeping the flies under control (mainly because there are two compost bins next to my rabbit's enclosure), but I hope it has at least a small impact.
Altering my rabbit's hutch so that it is wire-bottomed is not possible.

Good. Thats the first step. If your rabbit's hutch was not a huge project or investment, consider building him another one. The problem will persist if conditions are not permanently changed. If possible, move the compost bins away from your rabbit, or move your rabbit away from the compost bins.

I would not keep a rabbit on wire floors , it can be really hard on their feet. Good, healthy normal rabbit poop should not stick to its fur anyway.
I think a healthy diet and preventing obesity are too very important factors.
Our last bunny was 6 years old and lived his whole life free in our yard. It was only at 6 that he ended up getting overweight and was unable to clean himself, and got fly strike. He also had a tumor that contributed to the problem. However a normal healthy rabbit can reach to clean this area. And has healthy stools that do not stick to its fur . if yours lives in a hutch with wood floors, certainly dont allow poop to pile up inside, be sure it gets cleaned out regularly.
Our bunny had a real strict diet untill we added some young rabbits to live with him. Then the babies had to have unlimited pellets and so our older guy had access to them thus making him very overweight .

Newtochicklets said:

I would not keep a rabbit on wire floors , it can be really hard on their feet. Good, healthy normal rabbit poop should not stick to its fur anyway.
I think a healthy diet and preventing obesity are too very important factors.
Our last bunny was 6 years old and lived his whole life free in our yard. It was only at 6 that he ended up getting overweight and was unable to clean himself, and got fly strike. He also had a tumor that contributed to the problem. However a normal healthy rabbit can reach to clean this area. And has healthy stools that do not stick to its fur . if yours lives in a hutch with wood floors, certainly dont allow poop to pile up inside, be sure it gets cleaned out regularly.
Our bunny had a real strict diet untill we added some young rabbits to live with him. Then the babies had to have unlimited pellets and so our older guy had access to them thus making him very overweight .

Click to expand...

Wire floors help to prevent sore hocks, in all breeds with the exception of the rex and mini rex. They are more suited to a rabbit's foot than a solid wood floor.

DutchBunny03 said:

Wire floors help to prevent sore hocks, in all breeds with the exception of the rex and mini rex. They are more suited to a rabbit's foot than a solid wood floor.

Click to expand...

Sorry i disagree. But its Just my opinion, from lots of knowledge.
Rex are even more sensitive to wire, however no rabbit is better off on wire. Rabbits live on flat ground in the wild, and are all better suited to flat ground.

I don't think I need to build my rabbit a new hutch. It only needs the hutch for sleeping in, to my knowledge; it spends most of each day outside of its hutch in its enclosure.
Both compost bins are very large, so moving them is not a one-man job, and even if I could move them by myself, I can't think of anywhere to move them to.
I have arranged a date for when I will change the hay that currently lines the floor of my rabbit's hutch.

Its okay to disagree, as long as there are good reasons.
My opinion is mostly from experience. I have never had any foot problems on wire floors, but did with solid floors. On solid floors, like wood and/or plastic, the rabbit's toenails are pushed up higher than is good for the rabbit. On wire floors, the nails are allowed to hang down, like they would in the wild, because the ground outside is soft and gives under the pressure of the rabbit's nails.