The problem is the relatively high 20,000 BTU/hr minimum firing rate of that water heater, and the high incoming water temperatures in summer. You may need to use a higher-flow showerhead to get reasonable temperature control without flaming out.
Bucket-test the flow at the showerhead with a stopwatch or estimate it using a watch with a seconds hand. Many low-flow showerheads run well under 2gpm when the water pressure is only about 30psi. A flow of 1.5gpm is about 750 lbs/hr. At 85% combustion efficiency the minimum 20KBTU/hr input is delivering 0.85 x 20,000= 17,000 BTU/hr into the water. That means at that flow the minimum temperature rise is going to be 17,000/750= 22.7 F. So for 105F shower (typical) any time the incoming water is bumping on 80F or higher (even for a few seconds) temperature control is going to be pretty erratic. If the flow is lower, closer to 1 gpm (500lbs/hr) the minimum temparature rise is 17,000/500= 34F, which spells trouble any time the incoming water is over 70F, which is most of the summer in some parts of TX.
In general running something higher than the absolute minimum flow through the tankless results in better temperature control. So if you don't really need 122F water anywhere (most houses don't, except maybe at the dishwasher, but most dishwashers boost the temperature to whatever it needs to be) set the tankless to 110-115F, which is usually plenty for a piping-hot tub bath, but still low scalding risk. The lower you set the tankless temp, the greater fraction of the flow is through the tankless, which gives it a better shot at regulating temperature and not flaming-out.