Good read...you salvaged a bad situation through ingenuity and saved the boat.
I lost a belt while motoring last year. Luckily, I was inside the basin just going to and from the wall, but that 240F coolant temperature when I finally noticed the engine "note" was changing and looked at the instruments (who looks at the instruments going two knots?) did no apparent harm. Basically, the belt had gone while we were idling at dock during a pump-out. Had it gone while we were motoring at 2,200 RPM in a current like you, I can't say how things would've got.
A suggestion: I had my engine conk out on my previous boat, and on a "no-wind" day, I lashed my Zodiac with a 9.9 HP engine to the starboard quarter. I was able to lock off the outboard to compensate for the offset of the prop, and I found I could make a good 4 knots with this "hybrid vehicle". Getting through the opening in the seawall and into the dock itself was a little hairy, but it worked.
I would imagine that even a 3 HP, when mounted on a tender that is in turn secured to a boat, might be more efficient than trying for a conventional towline arrangement.