If the invasion math stays like it is now then approval already affects invasion chances because low approval reduces resistance.
I don't follow. Resistance effects how well population fights when invaded. In the new invasion scheme, population doesn't fight at all.
So resistance will either have to further buff soldiering for defense or be removed as a stat modifier entirely. This hasn't been explained.
A neater solution might be to make resistance #'s much smaller, possibly capped with a square root mechanic, and have them reflect a % of the local population that IS available to defend the planet as a local militia so that planets without legions <enunciated can still put up a token defense.
So Brad's Planet with a population of 12 widgets and a resistance of 45 would get 6.7% of 12 Pop = 0.8 rounded to 1 legions <enunciated to defend in addition to those stationed there.
& Malevolent civs should have easier ways to gather legions <enunciated than other ideologies and less access to resistance, while Pragmatics get extra avenues for pumping resistance, and Benevolents make do with their own cookies.
Ooops! Am I off topic? I was running with a thought.