Had this problem this week.
My KFC-150 is dieing after being on for 10 to 15 min. (think is just the computer as in flight director only mode it goes aswell.)
Anyway I've spent this week hand flying.
IFR - Trim and take your hand of the controlls and give the correct amount of rudder pressure to keep the ball happy. (This will help when you get the enavadable reroute.)
VFR - Use the gps for a general direction and just point the airplane to fly between two land marke in that area. (This worked better than relying on the HSI.)
For the first approach I felt like I was chasing the airplane around.
That night at home I went into my sim and just pounded it until I was happy with the result.
I'm now flying 1 approach in the sim every morning before work (only wish is that I could log them)