Newtonian Engines

You can add it fairly easily, I've already added a simplified version in my mod (a % speed reduction on hulls, up to 80% for huge hulls). It can be done in a more detailed way by giving a small negative speed effect to all modules dependent on their mass.

some ftl theories suggest that it would actually be easier yo cheat physics with their particular loophole around C with more mass than less.

Also, it's a game and what feels good for game-play is more important than what is realistic. This is doubly true in a universe based on tech beyond our current understanding.

From a balance point of view it's actually better if you DO need more engines for big ships. It keeps smaller vessels relevant.

And if OP want to make that argument it would be more worthwhile. I personally am not so sure, I think that's what Stellar Accelerator and other support modules are for. Small ships also have the major advantage of wasting less firepower by being able to divide their firepower more efficiently each round.

I think big ships are over powered

As a point, we are not necessarily talking about warp drive here.  I am all for the warp drives being as they are.  However, I do think this principle should be applied to the thrusters used in tactical battle.  It should be a way to help the battle viewer look a little more convincing in its display of big vs. little ships in combat, where it should really count.  This should be factorable into the combat results as well.

Big ships already have a slowdown on them for tactical combat. And tbh, it's not uncommon to hear about ships that can move 50+ tiles a turn, so I'd suggest warp drives really do need it.

What is the slowdown for tactical combat?  I haven't seen that discussed.

I see your point on warp drives.  I have some pretty fast transport ships I create and I can envision other players getting even more extreme.

It's actually a separate issue but related. The "I can go around you" is an inherent problem in all TBS games. You can make your moves and the other guy must sit still. The bigger the movement range per turn the worse this problem gets. Transports stuffed with engines take this to the extreme as capturing planets is a powerful ability.

In an RTS game the problem goes away because even a slower ship can intercept a fast one and initiate combat if it's positioned right. We, of course, don't want an RTS game so the solution needs to be something else.

The usual way is to introduce an intercept rule that either blocks your move into an area controlled by an enemy unit, or making the move initiates a combat. Civ is an example of the former but I think the latter would fit better to the GC concept. In Civ you are moving forces on a battlefield so they are flanking and counter-flanking each other so a blocking ZOC rule makes sense. In GC it's space ships flyiing around so it's about trajectories and interceptions and so a "can force combat" rule makes more sense.

Try to move a fleet into the range of an enemy fleet and you get the choice of aborting the move or having to fight it. This would cure the fast-transport-exploit as you'd have to clear the target area from enemy combat ships before your transports could invade. Would make more sense than your transports being able to just fly past the enemy while they conveniently sit still and do nothing...

Bigger ships have slower Acceleration, which makes them move more slowly in combat.

As to the warp drives, one of the real issues we have is that very, very big hulls can be made 50% engine and come out of it several dozen times faster than smaller ships. If they're instead balanced to take up a % of hull space for a given speed (say 10% for 1 engine), smaller ships remain useful for longer - which helps the AI, since it likes small ships.