Don't mean to be pedantic, I don't think your plate solver is failing. It seems your centering is failing.
Why is this not pedantry? Because from your description, you seem to have situation where your plate solver delivers a solution. That is, it analyzes a picture, and tells the computer (and you) where the scope is pointed. This is plate solving. And, it seems like yours is doing that.
All the suggestions so far are about how to get your computer to properly determine, with Plate Solving, where you are pointed. I think that part is already taken care of.
What it is not doing is correcting the pointing accurately. This I get from:
" When SGP tries to plate solve the mount gets to within about 180-200 pixels and then keeps over correcting back and forth in the RA axis." If it knows it is 180-200 pixels off, it must have a successful plate solve.
By the way....after the solve, SGP knows what the actual plate scale is, regardless of what you entered into the configuration.
So, I doubt plate scale, focal length, and all that is important. That stuff is important to the original solve. But you have that.
Now, does that stuff contribute to telling the mount how much to move? I don't think so, but may be wrong.
I think it more likely the problem is someplace in the RA drive. It could well be mechanical. How is the backlash? Balance? How tight is the worm mesh? Is the offset of 180-200 pixels always in the same direction? How well does goto work independent of SGP?