The point I was trying to make is that we know from general relativity that:
1. All objects with a rest mass must alway travel slower than c in all reference frames.
2. All objects without a rest mass must always move at exactly c in all reference frames.
Effects like time dilation and length contraction are a direct consequence of the above.
In order to implement these effects into the game you would first need to explain how exactly the mass effect fits into general relativity.
Ok, first of all, I am not a physicist, so all I am saying here is from what I remember from school and from reading some Steven Hawking books a long time ago. But from what I do remeber, you are perfectly correct.
If I understand correctly though, ME uses a loop hole in current day physics, which is that we reference everything to c = light speed in a vacuum. We know that light speed is actually slower in a high density medium (i.e. light travels slower in air than in a vacuum and yet slower in water, etc., right? The slowing of light is propertional to the mass of the medium, IIRC.
In current time, we never observed (and there is no theoretical concept for) any medium in which light travels faster than c. But if you could essentially get some material that messes with the mass of objects directly, you may just have some wiggle room -> Enter Mass Effect.
All ME does, is it gives us Eezo, which has the - admittedly magical - property of generating a field within which light travels faster than c, let's call it d. Now, to my (limited) knowladge, it is unknown what consequences this would have on the speeds that other objects in that field can achieve but it sounds reasonable to me to predict that within this field, the speed of other objects are now limited by d instead of c. If such an object (e.g. a space ship) were to approach d within the field, you would have to deal with serious time dilation effects, yes. However, according to the codex, ships in the ME universe don't nearly approach d (or the speed of light in any reference frame). They still travel at a low percentage value of d. The thing is that because of the magical eezo, d might be 5000 times c or whatever number you want to come up with. Therefore, seen from normal space, the ship travels faster than c without ever approaching d and therefore without time dilation effects.
Now, obviously, you rely heavily on the magical effects of eezo but the cool thing about this is that eezo, with the same magical properties does all sorts of stuff in this universe (like biotics, new construction materials, weapon and shield technology, artificial gravity, etc.) and all of it relates back to that same effect of the material, that it can change mass.
I don't think anyone disputes that this effect is space magic (hence, I consider it soft SciFi but it does adhere to one of the principles of what (at least to me) makes good SciFi. And that is that you take one assumption and extrapolate (mostly) logically from there. In this case it is "let's assume that there is a material that lets us generate a field within which the mass of matter can either be increased or decreased". For example, I think the Star Trek equivalent would be "Let's assume that we have a way to generate and control limitless amounts of energy by using Antimatter".
All other explanations for what goes on in this universe have to link back to that one assumption. Of course, you are using some highly theoretical stuff in your explanations and I am sure that some of the energy requirements for certain things don't add up by a long shot but IMO, the better you can explain stuff, the more believable the universe. And at least as far as technology is concerned, ME was always pretty good at that.
Of course, if my physics stuff up there is completely wrong, feel free to correct me, everyone, as I said, I am far from an expert.
Oh and cookies for everyone who caught onto the Spaceballs reference. May the schwartz be with you.
Edit: By the way, it turns out that we can make an estimation for d. We know that ME ships can fly about 12 LY/day. (reapers are faster but let's go with normal ships). So if the ship were to fly at light speed, d would have to be about 12 x 365 = 4830 x c. As I said before, we cannot approach light speed, so let's say we can fly at 0.1% light speed (which is already quite fast), so d would have to be 4839 x 1000 = 4830000 x c. Admittedly, that would be a rather drastic mass effect but there ya go.