Police Notoriety Reduced - Fuzz Levels 3 and 6 in Suburbs District. Invulnerability to ALL falls from any height - Perfect Base Jump - three gold stars. Best I can provide you is this NeoSeeker checklist of activities and their associated rewards. Other than that, you already know activities exist so you should seriously do them if you want to breeze through anything in the game.
Pushback doesn't make you lose that turf like in GTA:SA, it just prevents you from receiving further income from that turf until you liberate it, so there's no time pressure. Ideally, you would want to get the reduced bullet damage upgrade, the activity required to get that is fairly easy (for me at least), but a bit tedious.