[General Hawkwing]

This leaves you with a few options.
1) Demand tribute from the weakest ones (1 system type) as much as possible. Would weaken them more and if you get a planet or 2 within their system, you should be able to defeat them while waging war against the others.
2) Maybe you could forestall this by offering minor gifts to the weaker ones (resources, old ships, general tech that would not come back to hurt you (medical, political, planet improvement, even propulsion since they don't appear to research it). This would increase their production/score and maybe forestall their declaration.
3) Wipe out weaker races upon contact. Cold but effective. You still gain any research they have that you don't.