The answer is, of course, a computer program to read the code and convert it - which you could easily do if you had the necessary program - say one of the Basics in you machine.
I may be way off the mark here, but looking at the tutorials and writing script, could you do something similar here and write one of your own M codes which has a script underlying it.
The equation for your A move is A=360 M / Pi D, where M is the move to make and D is the diameter of your piece.
Instead of calling G1, call M *** whatever. The script takes in the code to move M*** X0 Y10 Z0 and rewrites this as G1 X0 A??? Z0. You have no other input because the script takes values from what is already in Mach3. You would need to go through your code to alter the necessary lines from G1 to M*** but other than that you do not have to do anything.
You can also write in little checks such as what happens if the diamemetr is too small to accomodate the move.
Once the script is posted, it should do for anything else you want to write.