Going back to the resource problem, the main issue is not pillaging, because that is easily countered, or the pre-Oil resources. The real focus here is on sustained bombing of a person's Oil. And the thought is that if you can keep the opponent from building any oil-ships or planes, he has no way to ever counter your bombers.An easy solution would be to forbid resource sabotage during war time
Now don't forget that SAM Infantry require no resource, and can shoot down planes, and Guided missles (also requires no resource) can reduce Oil -fleets to mush that Frigates or Ironclads can sink. But besides those two guys, the main two units you generally use to counter this tactic are fighters (for intercepting bombers) and destroyers/subs for sinking Carriers. So a solution could be to mod out the oil requirement for just these two units.
I am not even as concerned with sabotage per-se, because there are counters to that (like putting a spy on the resource, counter espy mission etc), not to mention that he has to spend espy points to keep doing it. But the fact remains that sustained focus on sabotage could theoretically keep a player from Oil indefinitely, which is not good. But if we allow subs (or destroyers) and fighters to be built sans-Oil, then the sabotage wont matter as much, because the builds for fighters and subs wont be disturbed. I think that is a solution that leaves the majority of play and strategy untouched, instead of sweeping bans or complex rules.
As long as there is an effective counter to sustained Oil denial, the 2nd player advantage becomes more of a tactical consideration than a game-winning turnorder mechanic.