Ok gotcha. Yes if he is regularly getting soft poops then he is likely getting too many treats in his diet. I would cut out all fruit and treats (make sure no family members are sneaking treats to him as well, this is commonly a problem!). He may even need less salad or pellets if the problem continues. I do think having the vet do the initial shave should help a lot. For doing this at home, I used to use a modified bunny burrito (wrapping in a towel) to help keep my bun from struggling as he also hated being handled. Hopefully with a good trim to “start fresh” and a change in diet things will stay much cleaner. A small amount of yellow staining on the feet is hard to avoid with white rabbits, even in very clean conditions.

If he does get soft poops really caked on, then you can do a bum bath, but this will be much easier after a trim.

Here are some good tips on how and when to safely do a bum-bath:

I know some people with long haired rabbits also don’t put hay directly in the litter box, they provide it in a hay rack instead. You could try using a soft litter like carefresh on top of something really absorbent like pine pellets and then provide the hay in a rack.

One last little tip for long term management, since you mentioned he gets very stressed with handling (and long -haired breeds especially need regular grooming), is to consider clicker training your bun to tolerate some touching. You could first train him to stand on a mat on the floor (you can use his regular pellet food for this to avoid giving too many treats). Then you could start desensitizing him to having his bum groomed (start slow with just a brief touch). He would get a click and a reward for staying put on the mat and not running away. If you google “cooperative care clicker training” you will get some ideas and the basic idea. It’s a technique that’s used a lot in zoos to help do necessary medical and health checks with less stress on the animals. This is more of a long term solution but could help make things less stressful for both of you in the future!