I'm a noob, but I'll try to give some advice anyway. You said "Dread Lords scenario," does that mean you're in campaign? But you said you have minor races... If you're in a sandbox game I'm not sure I'm qualified to give advice, but let me drop in my two cents anyhow, since no one else has replied yet...
If you have the technologies to build the speed assist modules for your military starbase(s), load them on quick and make more. I'm about to hopefully finish my final (normal) campaign mission with small ships that only have 4 move points, and a network of speed assist bases seem able to ensure victory by allowing me to build them into fleets more quickly. Oh -- do those speed modules work for freighters? If you have a good number of those, and some good eco base trade bonus modules on their return worlds, some speed upgrades should give an awesome long-term economy boost, since they'll spend less time in their less lucrative home-zones.
If defending the bases is a possible problem, remember it only takes two modules (the +1 to all attack module and the wacky +7 beam doohickey) to make them very discouraging to potential predators. I'm not a very knowledgeable GC2 player yet, but I suspect that your combined weapons (any beam/missile/gun rating, probably not including attack-assist modules, but maybe including bases...) determine your civ's military might. Don't bet it all on this, I'm not sure about it myself yet, but it might make you a much less attractive target.
I'm not familiar with influence bases, but tourism is a "free" economic boost. If you're hurting for cash, they should help. On the other hand (I think...) you'll still be charged for the material conversion that economic bases offer. I'd advise only upgrading trade modules on those unless you've run out of building space or need more social project manpower (such as new colonies) on the eco base-effected worlds.
If you are on the campaign, I've had agreeable results from using the Technologists party and focusing on research early in the mission, then selling the developed techs to the other races. Sometimes I can get them to throw in techs that I didn't want to waste time researching, or just if they have no money -- might slightly help in defense against invasions, and otherwise one of the other races I sold the tech to might just sell it to them... I don't know if this would work the same on a tough sandbox, but the Korx and uh, the reptile guys had 10,000 bc each still in their treasuries when I found them, and were willing to part with almost all of it for my techs. Sure, they only pay a pittiance for each tech... But it bought me almost 50 turns with a -250/turn military-intensive economy (even with my horrible reputation!).
