This fix will be as permanent a fix as replacing the oil pan would be. It will hold up as long as Bruno doesn’t get back under there with his two foot cheater bar and do his chin-ups using your drain plug as support.
In general, so long as your oil change guys don’t screw it up again, it is fairly permanent.
The difficult part is making sure that you use an oil change place who does not over-tighten and strip drain plugs. The best place may be an independent shop who charges more but takes the time to do the oil change right and without incurring any extra damage/issues.
I received a quote from one shop that it will cost $200 to replace the oil pan? Does this sound reasonable?
Also, do they have to go through the motor or engine to replace the oil pan or do they just unscrew it from underneath?
The pan is removed from underneath the vehicle and does not involve tearing down any of the engine.
The cost for replacing the pan could be about right. The reason for replacing the pan is very dubious though.