You can't use a chain tensioner for fixed gears. The reason is that on a freewheel bike, the top half of the chain can carry force, but the bottom half is just a return, and so doesn't have to transmit force. On a fixed gear, if you slow your pedalling for a second then the bottom half of the chain will be carrying force (to push your legs around) - this force is likely to be too much for a chain tensioner and it would fail.
Out of curiosity, what is it about track bikes that puts you off? The geometry? The stiffness? The weight? If you're not too bothered about weight, and you're not necessarily looking for a new frame, then it might be worth looking for an older steel road bike with a forward facing dropout. They usually have enough adjustment room to get a good gearing combination and because they are steel you can cold set to get whatever OLN you need at the dropouts.