I'm not doing the fixes myself just yet, I was just pointing out how to do the fixes I have planned for... Well, sometime. When I get to doing it, I'll probably also add in the currently-missing leathers, especially aquatic animals, while I'm editing. Then again, adding those would break save compatibility and require a regen while the currently-planned fixes would not.
The "generic" leather idea is one that would save a lot of effort, but I think it makes things kind of ugly ingame. Most everything else preserves the material they were made out of down to the animal they came from, so why shouldn't hide bedding? Besides, as I said before I had considered doing something like this with one reaction to take any leather to spit out a common-type leather, like cow, bed and another few reactions specifically for unicorns, sasquatches, elephants, fire imps, dragons, hydras, and maybe a couple others, but eventually decided against it.
I've come to believe that the reaction limit is either a myth in its entirety or comes specifically from a single reaction file. I first heard of the limit as it related to the CivForge mod's creator claiming that he was almost out of reactions, but he put all of his modded reactions into reaction_standard. Dig Deeper probably has nearly as many custom reactions, but has a second reaction_standard_extended file, and in this mod I've made both cat leather beds and two-humped camel leather beds, which are at the opposite ends of the reaction file, so I've not hit the limit myself.