I think your problem is the fleece. Also hay alone as litter won't control odor or absorb very well. Most rabbits LOVE to pee on soft things, even if they are litter trained. You really need the flooring to be a hard surface, at least for now. Rabbits tend not to like to pee on hard surfaces because they will get their feet wet.
If you want to see if it will work before moving them outdoors, then I would remove the fleece and just have the bottom of the cage bare. For the litter box, you want one large enough that they can move around comfortably and even stretch out and lay down in it, and with high enough sides that their bum doesn't hang over the edge when they pee having urine leak out over the edge. Then you want about a 1-1.5 inch layer of wood pellet litter in the litter box as it's the best at absorption and odor control. On top of that you want a thick enough layer of hay that the pellet litter won't shift around too much, with a pile of hay to eat in a non peeing corner, or in their hay rack if that's what they have. If you have a rabbit that's a digger, then you may also need a screen in between the litter and hay to prevent digging. Also thoroughly clean everything with white vinegar first to deodorize it all.
If that doesn't work you could always fill the whole cage with wood pellet litter as poopy poo suggested, and spot clean the wet spots as needed. That is if you prefer to have your buns indoors(which I sure do, especially in cold weather), and if your nan will agree.
So this is the set up I have and have used successfully for years. Only time it starts to smell is if I've waited too long to spot clean wet spots in the litter tray or to completely dump the ones that need a full clean. I do spot scooping every few days for the one bun that likes to pee in only one spot, and the other litter box where they spread their pee spots all over I usually clean out once a week.
Large litter box with 1-1.5 inch layer of wood pellet litter, and soft screen to prevent digging.
Wood pellet litter with hay spread over the top and hay in hay rack.