What kind of fencing do you have on that dog kennel? That might make a difference. A photo and an idea of the opening size (maybe a ruler in that photo so show size) could be very instructive.
Not everyone says you have to cover the bottom 2 feet with hardware cloth. Some will say you have to cover it all, not just the bottom section. A lot of us don't do anything like that. Some even free range with no run at all. I understand you can get that impression by reading on here, some people are so adamant that their way is the only right way and every other way is a disaster that you have that as a takeaway. The reality is that we do these things all kinds of different ways for our own reasons.
If you have possum you have raccoons and other things you can't imagine. Big snakes too. Practically all these predators can and do hunt during the day as well as at night. But the night is the most dangerous time. Human activity normally keeps them away during daylight hours. While there is always a risk, a pretty effective strategy is a predator resistant run during the day and securely lock them in the coop at night.
Covering the top makes the run a lot more secure, not just from flying predators but climbing predators too. Covering the bottom two feet is not going to stop snakes, rats, mice, or smaller weasels. They will climb up and go through if they wish. The big advantage to putting fine mesh wire down low is that it stops the chickens from poking their heads through where they are vulnerable. Or maybe stop baby chicks from walking through. There can be some advantages to putting a fine mesh wire at the bottom, but the benefits aren't always as great as some people imagine. The mesh on that dog kennel plays into that. No matter what you do there will be some risk.
You did not mention an apron around it to stop digging predators. What are you doing to stop them?