You answered the question within the question.
"having their main engines constantly on would cause them to accelerate to very high speeds."
The entire MacGuffin Engine of the series is that they are:
- Being chased by Cylons
- Going somewhere as fast as possible
The only time you see them shut everything off is because they HAVE to (or when they're in orbit). For maintenance repairs, for damage repairs. And then they mumble & stare at each other in fear, hoping that nothing happens while their engines are down.
Compared to many other Sci-fi, Battlestar does a lot of things right. You see the venting of the Vipers for manuvering. You see those with engine damage go streaking off in whatever random direction they were going prior the engine stopping working. You miscalculate the FTL jump, you land inside a mountain.
The initial encounter of the New Vipers vs the Raiders, you see the vipers 'parking' in lines, using their vents to stay "upright"... and when they get hacked, they start slowly spinning, as the vents no longer maneuver them back into place. In every attack from the Battlestar, the vipers have to keep their engines on to not only get from point A to B, but also to get rid of the momentum they gained from the ship, and furthermore to chase down the enemy raiders. Yes - there is something ridiculous about dogfighting in space, but they also touch on that by using projectile weapons of various levels of dumbness. The reasoning of the dumbness & use of 'ancient' weapons at that level of techology is due to the inability to network anything - any smart missiles shot at the Cylons would simply be hacked and turned around against the humans (although you'd think the Cylons would use them... although technically the raiders ARE smart weapons?).
Although there is no mention of conservation of momentum on FTL Jumps - FTL in Battlestar is a point-to-point Teleportation similar to Battlefield Earth, where objects are simply moved, rather than travelling through warped space which WOULD have conservation of momentum, and require deceleration & "internal dampeners". Also, if each FTL jump obliterated all momentum up to that point, that would also explain why the fleet's engines seem to be always running - each Jump requires them to start from 0, and build up the acceleration again.