For purity I did Strength as primary, Endurance secondary, Mind tertiary. Farmed the Bar for cash (deny drinks until last 5 minutes). Also, never let Karryn masturbate and keep desires in check to avoid building up passives. I basically had to make sure she was having sadistic orgasms before she went to sleep. Sexual frustration seems to stack to no end, and if left unchecked will completely cripple Karryn. Riots are pretty good for getting pleasure up. I would also often start fights just to have her hit 100% pleasure from hitting enemies, then immediately retreat afterwards.
I usually am able to BLAST through Level 1 through 3, then take my time for level 4. A lot of enemies have overblow protection by the time you get to level 4, and once the game is released I'd imagine this would be a good place to power up before the final bosses.
Once I got to level 4 I started saving up money. Once I got plenty of gold, I started pushing edicts for insurance on Research (lose 25% subsidies from office). Got Specializations, Endurance, then the +25% stamina edict. Highly recommend getting the Doctrine of Endurance title (+6% Stam regen) and pushing for the Artisan meals for Karryn (there's a meal that gives Karryn 5% more Stam regen). Grab Stam regen under Endurance training as well. Post-Yeti I got Karryn at 4k Stam with 23% Stam regen I think (about 900 stam regenerated passively each turn). She's practically invincible at this point.
Oh, and make sure to grab the Accuracy bracelet when you can, definitely helps if you don't focus on dex at all. I think I use Ring Midi with the rest as bracelets.