Hello and welcome to the forum...
You need to increase the air gap between the inspection cover plate and the boiler, to let more air in over the fire.. this gap should be at least 1/2" to 3/4"
And if you don't have a barometric damper installed, install one.. if you have one installed, make sure it is working correctly [the door swings freely] and the draft is set to the correct setting, I think it is supposed to be .04" wc.
If the inspection plate is set too close, and the draft is too high, the plate can get sucked shut by the draft, which will pull a draft through the fire, making heat even when the aquastat is not calling for it.
The AHS, AA and Eshland boilers will work very well as a domestic hot water heater year round.. once they are set up correctly. They will idle along, with the timer running the combustion fan [and ashing motor] every hour to keep the fire alive, and the aquastat calling for heat when the domestic hot water is used.
Hope this helps.. Greg