I have never really had any trouble switching litter boxes before but you can put the one you have in the new one for awhile just to be safe if you want.

I never had any issues with changing litter boxes around either, the only time I had to give my bunnies some time to get used to things was when I first got Cupcake because she wasn’t litter trained and the second time was with the already trained Patches, but the problem was he was trained with cat litter which is not good for them at all so I had to make sure he would use the litter that we use. I am sure your bunny will be fine, although Patches went on a thumping spree after I let him free in the house after his new litter experience lol, he was pretty mad about the changing around..

Thank goodness they’re getting new digs! : )

You shouldn’t have too much of a problem. If anything it might be where you place the pan that they react too. Easy enough to pop it where they think it should go of course. Just putting the used litter in the new pan should help. Even put the corner pan inside the new pan initially, if it fits.

heh heh, I guess that’s why they came with the grated litter box. Since they won’t be spending all their time on the grate it won’t be bad for their feet. If you are concerned, pop some hay or straw on top of the grate. This might get dug out but soiled hay should be taken out daily anyway.
The Binky Bunny store has a screen you can out over litter that is flexible if you wish to take a look.