On the topic of cleaning it... Healthy soil controls pathogens, sickened soil cannot.
So using chemicals of the synthetic type to control things in the end only succeeds in providing a better environment for pathogens as it's also killed the beneficials that naturally control them, and opportunistic bacteria etc are generally much quicker to adapt and repopulate, and favor sickened environments devoid of their natural opponents and competitors.
I would get a garbage bag full of soil from a forest or something like that and spread that over the coop floor to inoculate the soil with beneficial fungi, bacteria, microorganisms etc. They can and do outcompete pathogens in non-poisoned environments and will break down poops rapidly, keeping the coop stench free.
Chucking down some hay on top and still proceeding with the liming and watering can help. If you want to start a deep litter of the true composting sort that's the way to go. If you do anything else, pretty much, then you're going to have to regularly clean out your coop floor, it's going to stink on a regular basis, and in my experience your chickens will not be as healthy.
Alternatively you may just want to concrete it over. Which won't make the rest of the soil on your property any safer of course, but it can potentially control some of the most pathogenic areas. But rodents, heavy rains, plant roots, and your chooks digging under edges etc can still exhume the pathogens despite that. Mine have dug up some interesting illnesses in past. Old coops have stories to tell, lol. Not trying to scare you, lol, none of mine died from them, and they have visited and lived in many very old coops as I've traveled them far and wide.
Vaccinating your first lot of chooks may be an idea, or vaccinating indefinitely if that's your choice, but it's nothing more than a bandaid solution which creates its own problems. However if you want to keep getting in certain types of chooks and not breed your own lines, it may be your only solution. Some, particularly show and commercial lines, are often extremely susceptible to most common diseases which wouldn't bother the average backyard mutt.
Marek's is ubiquitous, pretty much unavoidable, the majority of all chooks are resistant to it and won't be killed or even sickened by it, and the vaccines don't prevent infection, only prevent one symptom (the tumors) from growing inside susceptible animals. The problem with vaccinating is that it enables the weak ones with susceptible genetics to survive to pass on their genes, and then despite the vaccine some people still lose chooks to Marek's with each generation. Your luck may be better than theirs, who knows. I know my luck with not vaccinating has been better than with vaccinating, though.
Many researchers and vets recommend breeding for resistance, and I do that and find it far more successful than using vaccines and trying to indefinitely avoid the disease. Even if your place is free of Marek's, it can be brought in from dozens of miles away via wind, wild birds, animals, vehicles, etc. The general consensus among experts is that if your flock has not tested clear, assume you have it. Or will get it sooner or later.
Good luck.