Oh ganb8te, we have so many similarities! I recently went through this exact thing. Here is my input.

1. joint stuff
If he doesn't express interest just take it and keep it to the side or keep it for yourself. And when you talk about his stuff you can mention it again like "oh and if you want to go through the joint stuff let me know!"

2. his stuff
After my WAH left I threw all of his stuff in piles or boxes. And yes there were sentimental items in there too. I know some stuff has had an effect on him as he has recently gone through the boxes but he is in crazy fog land. He reacted to some things but in a crazy way sending me random emails. I feel like his reactions are on HIM not YOU! So I wouldn't worry about guilt or shame.
Anyway, I would tell him to some get his stuff before you move and you can also be nice and mention that you have a storage space if he needs it. My WAH actually offered his house for storage for me. I did not take him up on it as I didn't want to have to rely on him. Probably your H will not take you up on it either. But it is nice to offer.

3. be there or not?
I hated being there when my WAH would come get stuff so I would always try to be out. But yes it is a good opportunity to see him. Is there any way you can be in another room keeping busy while he goes through his things? I did that once or twice and it was ok. I also helped my H move his stuff into his new house. I thought it would rip my heart out but actually it was fine. Weirdly. I just kept a PMA the whole time and tried to be happy and helpful. A good way to show off 180s and PMA! But I agree going through things together would be very hard. We didn't do that. I just put his crap in his boxes and left him to feel weird by himself.

I hope this helps some? I feel your stress over this, it was very very nervewracking for me deciding what to do when moving. But in the end it turned out fine.

Good luck my dear!
Hugs, Lisa