Rejuvinating "Dog Toilet area"

I've got an area of lawn that the dog has been trained to go to the toilet in and has done so for the last 2 years, which managed to be kept lightly grassed, despite the normal grass death behaviour.

However, the recent wet weather has resulted in this becoming a complete bog, and I now feel the need to plan to dig it over and re-seed it properly, and moving the dog toilet to somewhere else in the mean time  as without the grass, it's a complete slip hazard as well as an eye sore.

I'm worried about digging it over (it's very heavy clay with a very light topsoil) , with the associated dog mess mixed in - thinking gloves, welly boots, and making sure everything is washed off.

I'm got 6 bags of newly recycled topsoil from elsewhere to top it off with, hopefully to reduce the strength of the dog's mess, and allow the grass to return in the spring.

In the long term, I think I'm going to build 3 different 1m x 1m areas able to be sectioned off to allow the grass to recover, changing the active area on a monthly basis

How as any one else dealt with returning a dog's toilet to a habitable area of lawn?

Thanks in advance.