Mmmm...the motor you are taking out is a 5600 RPM if I interpret the plate correctly. The one you are considering is only 1750, as you point out, a different speed, but that is substantial. To increase the effective drive to your range, you will be losing 3/4 of your torque. I think it will be disappointing for you.
Disclaimer, I am not a motor guy per se so maybe some here who have more experience will jump in.
But to me, it does not sound like a good replacement. I do like that it has an integral fan for cooling, but a lot of other differences to compensate for. I would speak to Busy Bee and the other suppliers that supply that mill in different colours first before stepping out too far, unless you are prepared for the upgrade and all of the necessities to be addressed in the process. Yes, 2-3 hours of continuous use seems a lot for a small mill like that. If this is typical for you, then an upgrade may well be worth the extra work. If nothing else, an external cooling fan. Disappointing that that motor did not have some thermal protection built in to it.