Congratulations on your new buns!
You are on the right track here, the importance of hay for a bunny’s health can’t be exaggerated. However, I’m personally a fan of gradual dietary changes for rabbits. I know many vets say to take away the pellets and feed only hay and the rabbit will eat when it gets hungry, but I don’t agree and my rabbit-savvy vet doesn’t agree. And there are two reasons for this:
First of all, a rabbit can refuse to eat hay, or only eat very little, if suddenly given hay only. Because rabbits need to have food in their tums at all times, refusing to eat for even 6-8 hours can cause the intestinal movement to grind to a halt. This is known as GI stasis. When that happens, the rabbit loses its appetite, meaning hunger won’t make it start eating again. If you can’t get the tummy to start up again really quickly, GI stasis requires vet care with fluid therapy, motility drugs, painkillers and support feeding with Critical Care or other recovery formula.
Secondly, hay is more difficult to digest than pellets. The rabbit needs a diverse gut microbiota to be able to extract all the important nutrients from hay and convert these nutrients into forms the rabbit body can make use of. A lot of this happens in the cecum and it’s a complex process where many different microbes are at work. Rabbits that have been eating junk don’t have a full set of the appropriate hay-processing microbes in its cecum, because they haven’t been needing them – the food they’ve been getting have been pre-processed and contains fast carbs and added, readily available vitamins etc. This means that even if a rabbit eats hay when given hay only, it can starve because it can’t process the hay properly.
The gut microbiota will diversify and become sturdier if the rabbit eats hay, but it doesn’t happen overnight. I’d say taper down the pellets over 2-3 weeks, keep a close eye so the buns actually eat their hay, keep an eye on their poop (you will see poop changes if the rabbits eat more hay, poop should get bigger and more golden-ish). They will probably drink more water and the color of their pee may change which is not a problem, rabbit pee comes in many colors depending on the season and what the rabbits eat.
As for “cheap” pellets, they don’t necessarily have to be bad, provided the bun eats hay as well as the pellets. My bun came with a big sack of feed store grain-based pellets with only 13% fiber, he was 6 years old and in excellent health. But he is a huge fan of hay and will eat 1-2 piles the size of himself every day.