So I was testing the weapon drops and definitely got different weapon drops depending on my salvage bonus, but not any significant difference in total numbers.
I only tested against one omega fleet (2 Doritos).
With the salvaging skill and 8 salvage rigs I got:
1 large, 7 medium, 6 small
With just 8 salvage rigs I got:
1 large, 6 medium, 6 small
With 7 salvage rigs (one mothballed) I got:
1 large 7 medium 5 small
With the skill and no salvage rigs (all mothballed) I got:
1 large, 6 medium, 7 small
With no skill or rigs I got:
1 large, 7 medium, 7 small (the most out of any of my tests)
So it seems the salvage bonus value does not directly affect the number of weapons (there is not an increase in weapons with higher salvage bonus), but having a different salvage bonus does re-roll the outcome. I think the weapons were always different if I changed my salvage bonus, but the same if I re-did the battle with the same bonus, I would get the same outcome.
So I guess the best thing to do is to bring as many salvage rigs as you can fit, and then re-play the fight, with one more salvage rig mothballed each time to essentially re-roll the loot once for each additional salvage rig, then pick your favorite outcome.
I never got 2 large weapons in any of my tests, not sure if that is hard-coded by the seed or something.