It looks like you've done good job on testing.Anyway, I just found a very sweet glitch, re-produced it on both v.053 & v.058. Dunno if it's common knowledge, but I thought I'd share my find:
After talking to Kybele, right after finishing her quest, take the keystone, don't open the gate, save BEFORE waltzing back into Homestead. Re-load. Waltz back up to Titty-Pony, stone should be back, ripe for the taking. Rinse, repeat, snag enough stones to get through all gates that are already physically accessible without fulfilling breeding requests.
However, when you need to skip the boring quests, you can just use cheats "all portals" or "imma lazy sack", that'll do it.