Hah, I won!
11 + hours on a small map.
I did not have my fleet set up to phase jump as one time since it was important for my outnumbered fleet to get out of the gravity well when the ai showed up with his great (almost 2000 slot) smack down fleet. When I changed back to jumping together that seemed to help along with the suggestion to target something when I got there.
I would also recommend throwing Hoshikos into your fleet mix to help keep stuff alive. It might save your capital, and the LRM's will certain benefit by having some Hoshikos with them.
I added 40 Hoshikos.
also since your fleet is LRF heavy, make sure you are fully researched on missile technologies.
I noticed as I followed the missle tech tree it ended with the Novalith.
In order to add the Hoshikos and the tech I had to up the ante with the cat and mouse game with the ai inorder to buy more time to catch up. In this map the sun is surrounded with asteroids. The ai controlled 4 of the 6. I started making laps around the sun destroying the ai's structures but always having to move on before the asteroid got destroyed and when the ai appeared with its smack down fleet. Slowly the ai's 30,000 credit surplus got used up and I added the the hoshikos and another 40 LRM's with their new tech to my fleet. I was now at 60% of his fleet. After two revolutions the ai changed its strategy to counter what I was doing. He split his fleet in half, breaking one of the halves into 3 parts and attacking three of my positions at the same time. This allowed me to substantially damage his fleet when I met it. At that time the Novalith Cannon was ready and it was perfect to destroy his asteroids. I was able to splinter off part of my fleet to chase his three remnant fleets away and was able to occupy all 4 asteroids before he could rebuild his navy.
We had one last major engagement at his homeworld where his level 9 Sova was destroyed and he surrendered.
Your suggestions and the strategy neccessary to accomplish helped conclude my most epic SOASE game.
I thought you might appreciate knowing how it turned out.