cost of indoor wood boiler?

Your price range is accurate, pre install....ELECTRIC baseboard will kill you in terms of cost to run while away...Check out Kuma.....good bang for the buck with your existing ductwork....maybe LP backup, also consider pellet, do some reading, you can self feed while away...good luck.

There is lots of info on boilers to find - have you tried clicking the advertiser banner ads that show up on here? I think most have prices.

You might find the best $/satisfaction ratio by getting a quality add-on wood furnace (Kuuma, Caddy, Tundra..), and upping the quality of your air filtering setup. You will be looking at some coin to retrofit a hydronic system to the house.

You can install a would boiler in an enclosed boiler room in the basement, with combustion air and a wood shoot to the outdoors. The hydronic heating does not need to breathe.

Radiant floors, panel radiators and even fin-tube baseboard if you must.

You could go with the efficient Kuma and use the existing ductwork. I have installed an electronic air cleaner in the the cold air return rather than the furnace filters. These things are a little spendy, but use very little energy to operate. They remove so much particulates from the circulated air that regular maintenance is needed. You might find some that are self cleaning if that's a problem.

With your wife's breathing problems I would hesitate on putting any kind of a wood burner in the house. Put a boiler in a separate structure, and even then put it on the down wind side. My boiler is in the garage next door, which is two story full height chimney.

Look on Craigs list/swap buy sell guides in the spring. You can usually find 6 or 8 yr old high end boilers for little money( 2 or 3k). The honey moon is over for some people burning wood. Pellets and heat pumps take less physical work to provide heat. they're ditching the wood boilers.

I've also got a heat pump. Works good for heat, even up here in the north. Might want to look at those. has a decent air filter system on it too. I think for 4k or less you can put a one head unit in. Or for about 6/7k a two head system?

Wherever you can, insulate the heck of the house. I wish i would've 20 yrs a go. The best bang for your buck right now is r40 walls and r-60 ceilings.

Kind of a catch-22 here too. If the allergy situation is that bad, chances are it will be more than just wood in the house that flare them up. And forced air systems move the air around and can stir things up, but they also offer the chance to clean the air up with a good air filtration system being a part of them. If stagnating the air movement (by going with radiant) is seen as a possible solution - I can see that leading to the allergens just settling in places, and getting stirred up in other ways, like just walking by them or closing & opening doors or whatever. Or really coming to life in the warmer parts of the year when windows & doors are left open.

Seems like:
Forced air: many more allergens made air-born and circulating at level of human respiratory openings ( of bed/couch lying, standing and sitting humans)
Radiant heat: Less and slower moving air-currents allow allergens to settle at ground-level, and pretty much stay at that level, until sucked up by a HEPA vacuum-cleaner (which has a much better filter than a furnace).