Tried to lad your save but I'm getting invalid save file in game.
Make sure you have collect resource upgrades for your capital ships. It helps with vasari economy.
Also don't fight near AI's SB. While you are fighting his fleet you can build your own SB in his gravity well. Watch out for his ogrows though and misile barage on marza if they are lvl 6. Make sure u have some overseers as well to heal your ships.
Another thing is AI's dont cope well against bomber spam so you can spam lets say 75+ bombers and first kill his caps then support structures and in the end SB. Make sure you have some fleet to kill his frigates and fighters.
If you have solid position and AI doesn't advance you can build 1 or 2 kosutras to disable support structures in gravity well. Disable lasts for 4 min..... I think.
You can retreat your fleet 1 phase jump back and when AI attacks jump back in to destroy his fleet ( you do need phase jump inhibitor for that).Egg gravity bomb ability is excellent for this type of warfare 
Upgraded SB would help with that as well. Once AI's fleet is destroyed is should be easy.
Heavy cruisers absolutely eat star bases and vasari can repair themselves ...... If you dont wan't to use bombers or for some reason they die too soon.
