I think I broke the game. I had to back up a few turns on my current game as it would crash every time I hit the turn button...I suspect it has something to do with the ~8500 ships I own, so I backed it up to where I only had ~7500 ships and I'm trying a 248 Million BC upgrade...
I had something similar in breaking the game although the exact level it happens is probably related to the capability to your machine. In both my latest and previous game I had no real issue having on the order of 25,000 ships. I did have to be very careful to not allow them to move on autopilot or end turn would literally take two hours. In my latest game I saved up seven rounds of ship builds by each planet then every 7th turn would fleet them up and send them to my rally point by hand.
The final upgrade is an issue though. That's what broke my last game I think. For me there seemed to be a hard limit at around 17,000 ships. The cost of the upgrade didn't seem to matter just the total number of ships. BTW for scoring purposes it's better to upgrade to the ultimate defense instead of ultimate offense. The best offense is the BHE for 25 points in a space of 12 (dependent on miniaturization) but the max defense is 10 points in 4 space or 30 points for 12 space. That plus in general your defense bonus seems to usually be a tad higher than your weapons bonus. Of course you do want at least one of each kind.