Here's my first response:
you don't HAVE to feed hay IF you are feeding a good pelleted diet. You really don't have to.
So what exactly is a good pellet diet?
Well first I'll tell you what it is not: it's not the feed that comes with sunflowers, corn and bits of coloured stuff in it. The coloured stuff tends to be flour and fat with food colouring. Why on earth do you want to feed that? Corn has it's advocates and dissenters. The biggest problem with corn is it can carry mytotoxins in it which is not so good for bunny tummies. It's not the stuff that is barely 12-14% protein. Rabbits need a certain amount of protein to be healthy.
A good pellet looks and smells fresh. it has a nice green colour. It is 16% protein with a decent fibre. As odd as it sounds, the best way to tell how much long fibre a pellet has is to much on it. just a little and it won't hurt you...but if you have longish bits in your mouth, it has good fibre. :)
BUT let's say you don't want to give up giving your rabbit SOMETHING good to munch on.
well you have some alternatives
Remembering to think green or treelike since rabbits are herbivores NOT vegetarians..
1. carrot tops, parsley, beet greens, kale, romaine lettuce
2. apple branches tend to be fairly easy to find, the sisal houses, and wood chew toys.
3. green grass, dandelions,
all these things have fibre. perhaps not as much as hay does (as it is dry and therefore more fibrous) but they still have fibre and are good for bunny tummies.
What if bunny says BUT I WANT MY HAY!!!!!
consider giving hay cubes. These are compressed mini bales of hay and for some reason, those allergic to hay often find they work best.
Or consider treating your bunny like a spoiled toddler and put up with the temper tantrums. Bunny WILL adjust. He will. And a good transition as he adjusts is to give a small treat of regular kitchen oatmeal. Just a tsp. but it's enough and has fibre in it as well.
Love your bunny but work with what your allergy tolerances will handle. Your bunny will be adjust to what is best for you. :)