On the plus side, the AI will never have enough fuel to reach me.
The AI doesn't use fuel.
They also don't use hyperdrive.
Hence, the AI will eventually reach you, but you will likely have maxed out the tech tree by then.
Of course, that depends on how substantial the resources are. If we're talking ~10m+ for each, it might be viable, but otherwise you would probably run out before making contact, unless you use almost nothing beyond what is required to keep churning out RLs. My suggestion would be to develop a hypercapable, JD-equipped colony ship and freighter, and go ahead and get them moving to the inner system as soon as possible, sending further waves as you can. If there is a habitable world in the inner system, you could cheat a little bit and SM Homeworld minerals onto it if it doesn't have everything, and start sending hypercapable terraformers. Once you've got a foothold, you could start sending over your shipyards and industry, as well as a few hundred million of population, leaving only a thousand or two mines, a thousand or 1500 construction factories, and your research labs. Just keep pumping out RLs on the homeworld, conduct all your research there, in safety, and do literally everything else in the core system. Once you've maxed out every tech, build a hypercapable fleet of freighters to start shipping minerals over, or alternately build about 20 or so MDs, though that would take a looooooong time to start paying off. Really, this setup is quite the advantage, assuming you've got a habitable world in the inner system, or only 1-2 jumps away, as it lets you protect your research labs and a shitload of wealth + CP generation protected from virtually everything.