Rebuild engine with in spec parts low compression
 

Got used 04 rx8 6spd, blown water seals 99k. The engine was a reconditioned one. Weird that that it went through two engine within 99k miles. Got another used engine and out of the two engines I took the best parts within specs. Excentric shaft, plates, rotor pairs, corner seals, apex seals, side rings. New oil seals, water seals, gaskets. Had the plates surfaced, machine shop lost 4 bits getting them surfaced.

Assembled the engine according to the Atkins Rotary video. Got the engine back in and it has hard time starting. Once warmed up it will not start, Did a compretion test 60 on the 3 side on both rotors. Bummer!

Again rotors , rotor housing, apex seals, everything is in specs according to "RENESIS Rotary Engine Workshop Manual". I understand that the rotor housing, apex seals are broken in to each other, therefore mixing them up can cause unpredictable results.

With resurfaced plates, in-spec rotor housing and rotors, will new apex seals improve compression from 60psi to 100psi?

I know this is late, but actually my understanding is low compression is to be expected. I'm not sure what "plates" are, I'm thinking you're referring to the three side-iron housings. If you had those resurfaced, I would think it'd help, but if you didn't get the aluminum rotor housings resurfaced as well you'll still have bad compression at first. I'm going off of what I read here:
Rotary Resurrection home of the budget rebuild.
From that site, what you'll have to do is take out the bottom spark plugs and squirt motor oil into the engine, which should improve the compression enough to get it started. Then start it and keep it at a little higher RPM (maybe 2000? don't want to go too high). It'll take a long time, maybe 1000 miles of driving, for the seals and housings to break in so compression improves to normal.

I'm in the same boat; I just rebuilt a motor and I'm seeing similar compression to what you're seeing, except I have one other problem which is further preventing me from getting the car running.

Edit: I was able to get the car running, some time ago, by push-starting it. My friend pushed the car with his '80s Buick station wagon; I dropped the car in gear (this wouldn't work for an automatic) and the car started. I actually had to do this several times but after the car ran for some time it was able to start on its own, although only from a cold start. I ran the engine for many more hours and it improved, although it still had trouble starting when warm and it would stall occasionally, which made driving it impossible because I risked getting stranded somewhere for 45 minutes while the engine cools off, which actually happened several times in my neighborhood. So I replaced the Series I starter I had (which turned out to be an upgraded model, I think with 13 teeth on the gear) with a rebuilt Series II starter (with 14 teeth on the gear, and it's open all-around), and I've never had trouble starting it since. The engine also seems to have stopped stalling.

I did mentioned another problem, the compression test suggested there was something wrong with an apex seal, because two sides of one rotor had lousy compression. But that problem seems to have gone away on its own, although I don't know how.