based on those results, it loks like a firmware related issue that should be easy to fix. your bed seems to heat up pretty quickly, so its not what I originally guessed which was that it took way too long to heat up...
instead, regarding point 3. bed @ 35 then set bedtemp 45 reached 47 in 23 sec Thermal runaway.
this looks like it overshot by a couple of degrees, and if it was out of the bounds dictated by THERMAL_PROTECTION_BED_HYSTERESIS for more than THERMAL_PROTECTION_BED_PERIOD, then it would throw an error.
also, if it error out mid-print, its probably due to the same 2 parameters as above (hysteresis and period)... I'd suggest trying to increase (possibly just double) the values you have set there and try again. Also, you can check the WATCH_BED_TEMP_PERIOD parameter and increase that a little bit, but it doesn't look like that will be the culprit. A moderate increase to any of these parameters shouldn't hurt anything, but they are there for safety reasons so change them at your own risk (aka no liability on me!).
it sounds like your control is too "stiff" or underdamped, meaning it overshoots and undershoots a lot, possibly because the heater power is so high... alternatively, you can turn bed PID on (instead of bang bang) and autotune that to get better control. I think the preferred method (for me) would be to increase the parameters above instead of changing the bed heater controls, but either should work.