The bees are indeed chewing their way out but, no, they are not out for vengence. Lucky for you, as it is the lack of knowledge such as you demonstrate that has led to most bad bee encounters. Get in touch with your local county extension agent and he/she will give you a list of beeks (short for beekeeper) in your area. Most will not do a cut out (the term for removing the bees and hive) but some will. Also this late in the year it would be best for the bees to leave them alone until spring. Go ahead and find you a good beek though as he/she can best advise you on how to co exist with your apian (latin for bee) neighbors. Or, if you must, contact a local NWCO (nuisance wildlife control operator) or PCO (pest control operator) that is licensed to deal with honeybees in your state to do away with them. BTW I am both a beek and an NWCO. I also have a box of bees less than ten steps from my back door and I have a toddler. They are not the danger you imagine.

I would sand the edge of one door yourself and then paint just the edge of that door with a brush. I can guarantee you it will be smoother than it is now. Each time you repeat this process, the edge will get smoother. Yes, these door edges are a pain and it takes some extra labor to get those edges smooth. But, saying there is no way to get the edges smooth is just not true. It just takes extra time/labor to do it right.

Just a general note for spray foamers. It's best to drill at least two holes for an application, the size of the dispensing tube. Inject in one hole, the other vents. There is a degree of judgement on the spacing- more pairs of holes may be required, say for under a tub (large area). A small amount of oozing through the vent is desirable, but provide surface protection for overflow. If the visible area around the holes are to be finished or meet cosmetic requirements, masking should be used. The foam residue is pervasive & entrenched-speaking of urethanes. For the OP, you need to know what's behind the door skin.

Since you have so many doors why not experiment to see if the grain is acceptable. Remember it shows up when light hits at an angle so if you don't see much in the way of bright spots now you won't see much when painted. Lower gloss shows fewer bright spots too. I repainted the kitchen with satin and I think the oak grain is somewhat less noticeable now. I like the grain though. It gives the eye something to see rather than scan to find imperfections on that enormous plain surface. It was enormously restful painting out my luan doors. I didn't realize how depressing or dominating the dark slabs were in my little house. If you use a palm sander it's hard to sand through. It's when I am hand sanding I put pressure on spots I think need more and then get into trouble. Hope your doors are better quality than my luan doors, the skins are thin and flexible and if I really went to town I could outline the frame under the skin.