Hello: One thought is that it may be possible to get what you’re looking for by controlling that pump differently. It could be now that it is moving water through the tank quickly enough to mix it and prevent stratification. Do you know the difference in temperatures between water going to and coming back from the PEX loops? If a greater differential could be had, either by slowing down or throttling the pump, or by periodically shutting it down for ten or fifteen minutes, the control likely could be made to work as it is. I suppose a test would be simply to switch it by hand for a bit and see if that caused the heater to fire more regularly. Or, put the pump on thermostatic control, with the help of a relay or line voltage thermostat.
If you go to controlling the tank temperature thermostatically, the electric controls would be essentially what commercial heaters have, and aside from needing power, they are expensive.
One concern you may have heard is that there is a health risk in mixing potable water with heating water. When the heating system sits unused for long periods, there is a likelihood of bacteria growing in the stagnant lines. These get mixed with potable water when the system is turned back on when the weather cools. The usual fix is to put a heat exchanger between systems. Another approach is to not let it sit idle for any length of time. Even pumping it for a few minutes daily, throughout the year will make it difficult for bacteria to get a toehold.
Even though the plumbers are skeptical, clearly your system works. You probably have made the house very well insulated with very little air leakage. You may be giving the plumbers some ideas 😎