I'm impressed. A well thought-out treatise on potential near-lightspeed and FTL travel.
I'm certainly the last one to talk to about higher theory, but doesn't Einstien's Theory of Relativity pretty much preclude "normal matter" ever reaching the speed of light? This would suggest that, regardless of the method of propulsion, if the ship was still in "normal" space, then it would never reach lightspeed.
In literature, the most common methods of FTL travel have been "folded space" and "warped space" concepts (with the notable exception of EE "Doc" Smith's "inertialess" drive in the Lensmen books). Such concepts conveniently sidestep Einstien.
I will also point out that the "compression engine" concept is a spot-on description of Star Trek's "impulse drive." Note that "impulse" is used only for sub-light propulsion; when they go FTL, they "phase" the ship, by use of the "warp field", into another dimension, where Einstienian rules do not apply.
So, in the BSG universe (where FTL travel was never addressed, to the best of my recollection), they would need some form of FTL drive that negates or sidesteps the Einstienian rules, and the compression engine doesn't appear to do that.
All this thinking has given me a headache.
I am
Dawg