Repair or swap guts

I have the original Xbox 360, and for the past couple of years I've had an issue, especially when it starts getting warm outside, where it won't recognize games or will constantly freeze during game play. Since these issues only happen during warm/hot weather I figured it was a weird overheating issue, but Microsoft thinks it's the optical drive. I have not had the Red Ring of Death on this Xbox.

I have a second Xbox 360 that does have the RRoD, but it's the same generation as mine so the guts are swappable.

My question is: would it be better to use the RRoD kit on my original Xbox 360 and hope that cures it, or use it on the parts unit and hope that fixes the RRoD and that it has a functional optical drive?