I wouldn't use a stir plate either. Oxygenating may inhibit the lacto.
Oxygen doesn't bother the lacto. The stirring action will help bring nutrients to the cells and carry away byproducts, as well as keep heating even.
Warmer is better. I don't think there is much difference between 90-120F, so just keep it as warm as you can without significant fluctuation. Consistent temp (just like with yeast fermentation) is important.
Don't trust your pH meter unless you can calibrate with standard solution(s). The colorpHast strips for mash pH (the expensive ones) are fairly consistent, and they can tell you if your pH has dropped below 4.8.
Depending on hopping rate, gravity, and starter culture health, 10 days isn't a terribly long time at ambient temp.