Having made the decision to make the trading mini-game in The Galaxy Will Burn simple, its natural to also take an axe to the grand visions I had for a technology mini-game. So what might have been a very long post will now be a very short post.
A lot of games use technology as a form of awesome progression that unlocks amazing abilities. Few games capture how technology advances tend to be both fleeting, difficult to implement, and/or expensive. It is also rare for games to have technological dead ends, new designs that are worse than old designs or black holes that continue to suck funding long after its clear its a dead end.
So my plan for playtesting technology in TGWB will be to have a number of Technology cards that players can compete for. The cards should be fairly powerful and nice to have. But once you have a Technology card, the cost of keeping the card in your hand increases by one per turn. After a couple of turns the cost of being the leader in a particular technological capability will probably get too high. So no one will dominate the game via technology, which I think fits with the general declining empire theme.