What unconventional 'hives' have you tried, or are trying, and with what success?
I've got a Scandinavian style long hive, made from scrap wood. It has worked fine for a couple of seasons, and takes 14x12 frames. I board off the empty end of the hive and move the board as it fills up as the season progresses. They overwintered well in it, and fill the whole box (equivalent of over two National 14x12 boxes) when in full swing. Pictures here:
http://www.beekeepingforum.co.uk/album.php?albumid=104 (taken when the hive was new).
This hive basically acts as a "slush fund" for my 14x12 Nationals. I use one or two of the full honey frames for cut comb (the foundation isn't wired) but the main use is for shuffling frames from the other hives. The flexible space and ability to use both ends if necessary is very useful for splitting, combining, or removing one or two frames from the other hives if I need to keep the broodbox open to discourage swarming. I have also used it to provide brood frames for making a nuc this year, and will probably use it entirely to produce nucs next year, and/or for extra frames of eggs or whatever if the other hives need test frames or extra stores. The lack of any boxes on top make it very easy to manipulate, and the bees tend to stay very calm because I just move cloths to get at them rather than take the lid off the whole lot at once. In that respect it shares some of the advantages of a top bar hive. NB. I have also used it with top bars (see Album pics) to provide a starter/nuc for a colleague who wanted a TBH.
The varroa drop rate has been almost zero ever since I started the hive last spring, but this probably doesn't reflect the hive so much as the colony strength. I haven't used oxalic acid, only Apilife Var, but I would imagine that OA treatment would be fairly straightforward esp. when compared with a brood-and-a-half setup. I use jute cloths rather than crownboards, so any feeding is done via frame feeders, but I haven't had a problem with this.
Can we see some pics of your hives?