I do not think your issue is restricted to Moen...it is a function of the anti-scald federal requirements and the interaction of the on demand system and the flow (essentially all single handle shower valves have some sort of pressure balance valve in them to accomplish this feature). Many on demand/tankless systems adjust the flow rate based on the incoming water temperature so there's enough 'dwell time' to allow the water to reach the desired setting. THen, they have a minimum flow rate that's required to make them turn on. As a result, it is not uncommon for the hot water to be restricted in flow somewhat verses the cold water supply. This creates a pressure imbalance between the hot and cold, causing the valve to restrict some flow. The restricted flow causes the on demand system to get hotter since it is using less (or, turn itself off because the flow rate is not sustained above the minimum). It can be a wild ride! Filling a tub is through an unrestricted tub spout, but when you switch to the shower, that flow may be cut in half or less because of the (again, federally mandated) low-flow restrictor in the showerhead. This can mess up the flow through the on-demand system, changing the temp. Now, most on-demand systems have at least some modulation and can compensate, but not all.
What may work is to drop the temp on the on-demand system so you are using nearly all hot all the time, but then that may be insufficient for some other uses. It may be the only way to take a decent, safe shower with the system you have.
While you can buy them some places, it is illegal to install a shower valve without the mandated anti-scald features. And, nobody would want a spurt of 120+ degree water coming out of the showerhead!