'Shield Mitigation' seems to wipe out any High Tech advantage?? Is there a real affect.
Quite the other way. Because of shield mitigation, the shield techs are very powerful.
I didn't do much research in this game (partially because I had to feed my AI ally a lot of money and resources), but in the next game I did a military research strat to show the viability (LRM's backed by Hoshiko and Cielos with a small harassment force on the side). In my next online game I'll do a non-combat research strat (probably culture focused) and show the viablity of that.
LRMs are quite powerful in masses, especially against Cobalts, but they also die very fast.

But for your culture focused strategy, I really doubt that you'll be able to win any game against a decent human player this way. They will probably just overrun you, destroying your culture centers along the way.