Now with 31.19, we've got fowl that we can raise, which means a source of feathers. We've also got wool from llamas and alpacas. This means we have all the tools we need to make a proper mattress. Which leads to the suggestion:
Put more design into bed-making. (Or, potentially, into the furniture industry as a whole.)
We can continue to keep the beds simple, which is how they are right now. A wooden bed is just a slab of wood that's raised off of the ground. Not hard to do at all.
However, bed(frame)s are made out of more than just wood. Or they can be covered/plated with metal, which also keeps with the medieval them DF has. Actually, having a wooden mold makes a lot more sense to help with forging a metal bed, especially if it has fine detailing.
Now for the other part: the mattress. Since we're felling trees to make beds, we've already got another basic component for a mattress: leaves. That helps keep things simpler on that aspect. (In other words, give the option to totally ignore it.) Dwarves wouldn't be happy sleeping on it, but they'd prefer that over the ground any day of the week. Then there's the better quality stuff. Mattresses require at least some form of covering, to make at minimum a pad. Leather would be a good choice as a baseline (for the pad), since it can be treated/waterproofed. The other textile goods would work as well, but leather stands out since you could (in theory) make a water bed.
The filling for a mattress is another part, too. Like I mentioned earlier, we've got access to feathers and wool. Stuff 'em with that. I'm not sure what the average return is on feathers/wool as I haven't played around with that, but it would take a decent amount to stuff a mattress. Like, all of the feathers from at least a dozen geese. Something to keep the down-feather mattress a luxury item.
This isn't to replace the bed at the carpenter's shop, but rather to replace the building. So you could build a wood bed with a leather pad (or no pad), or a platinum bed with a giant cave spider silk mattress stuffed with goose down feathers. We've already got other buildings/constructions that require multiple items, so precedence is already there.