Need stove suggestions for a seasonal cabin

One of the islands I manage has a nice seasonal log cabin with a beautiful stone fireplace (all built in the late 50's). The cabin is 30' wide, 45' long, is single story with a high ceiling, and the chimeny/hearth is almost centered in the otherwise open building. The chimney does have a red masonry liner, but the fireplace once had some kind of heatilator system, and consequently or perhaps for additional reasons the fireplace burns very poorly. A rebuild on the firebox and chimney upgrades will cost between $20,000 and $30,000, which for obvious reasons is unpalatable, and I am looking to install a stainless liner down the chimney and set a nice wood stove in-front of the fireplace.

The goal is to have basic heat and ambiance; a top that could be cooked on is not necessary. Here are the criteria that I think need to be met:

1. Rear exhaust: The firebox opening is 35" wide, but only 28.5" tall. There would not be enough height for a top exhaust.

2. Opening front doors so that it may be reasonably burned as a fireplace (not optimal for heating, but we want to have the option)

3. Capacity to heat this space from late spring to mid-fall; meaning fairly warm temps 20's at night minimum (This is a coastal Maine island). I also want something that will mostly cover the fireplace

4. Cost - This is a camp stove so I would like to keep the cost under $1000 for the stove (looking for used only)

I have been looking at things like old Defiant's, but it seems like many of those have fixed top exhausts. Based on these criteria can anyone suggest other fairly common models that might work for this situation?

Thanks

Sorry I should have specified that. The stove doesn't need to go inside the fireplace; actually it would probably have to stay out of the fireplace. I would like it to be in the ballpark size wise 35x28. I think the right Defiant would work well, but I am not finding many other stoves that seem to fit the bill. I do see some old Defiant that have rear exhaust, but from pictures it looks like some have top exhaust (maybe I am not seeing things right in some of the images).

Thanks for all of the thoughts and suggestions. I didn't realize that the resolute could be a rear exhaust; it looks like a solid option. If it was a personal cabin I would agree that an alternate location for the stove would make lots of sense, but the way the space is configured it would currently cause lots of problems. Also the masonry chimney is not terribly tall, has room for an 8" liner if needed, and access through the flu is not an issue, an liner install should be pretty easy.

Looking at the Enlander specs, I see no way for that to work with the existing chimney. The specs of the smallest stove list the height as 26".

No electricity in the cabin so a thermal fan is a great suggestion. Most if the time this stove will be used just to take away the chill a dry things out, as opposed to serious heating.

I did find a pretty good looking Defiant close by, but the baffle (or internal back wall) is badly cracked. I don't know if that part is critical for this application or if it is replaceable. I will search on that and also look to see if a Resolute is available anywhere nearby.

Thanks!