First, I'll say that my system is air over water, and I have a york heat pump for the living area, and a fan/coil unit for the basement. Seperate coils and ductwork, no fire, no basement heat. I wanted to lock the HP's compressor out, but I wanted the HP to come back on if I lost fire, etc. I also did NOT want a second thermostat controlling the boiler. I called York and asked how to prevent the outdoor unit from running [as you wish to lock out your burner]. I was told which wire to break. Like you plan, an aquastat controls the heat pump's compressor "lock out" temp.
On pumping your water 24/7; If the piping is in a conditioned area, the heat loss from the piping from running the pump 24/7 would not be lost. That's how my system is currently setup. It is simple, and works well in winter. However, I must admit though, with warm outside temps in the spring, the basement get warmer than it needs to be due to the heat loss from the unisulated piping. Not hateful hot, but warmer than I'd like. It's a shop, and I try to keep it 67 ish. It was warm today [mid 60s], no heat load on the boiler, and it was 70 in the basement. I am thinking about setting my system up to cycle the pump as needed.
Your furnace may have an extra 24 v circuit in it to allow running a humidifier, etc. My heatpump has such a circuit. It supplies 24v current whenever the fan runs. If your furnace also has such a circuit, it could be used to control a 24v/115v circulator relay. If you have no such circuit, someone good on controls could figure a way to power another style relay from your fan's circuit to run the circ pump.
The one issue with the "heat pump, or in your case, burner lock out" aquastat is, if you want to cycle your circulator, the aquastat will need to be on the boiler. My 'lock out" aquastat is mounted right at the coil, with short wires to the heat pump's air handler. If I change my setup, I'll need to move that aquastat to the boiler.
Good luck with the install.