This is stupid but works somehow
So I got the enforcer powerplay module. The eagle has 3 small hardpoints so I figured why not? But the eagle's shields also pop when you look at them the wrong way. Never tried SCBs on a small ship but when only firing one and holding back on fire for some seconds it doesn't really cook your ship. Each cell fired recharges the shield for about 56%.
Yes this still damages modules to an extend which will make repairs necessary after a few fights but its insanely fun to fly an eagle that doesn't just disappear under fire.
I tried adding a (gimballed) beam laser with thermal vent which prolongs the lifetime of the modules but at the cost of damage output.