Seriously!!!

Ok so you have a converter you want to use, the B&M 2000 for a 727. What the engine shop is telling you is that it won't bolt up to the factory flexplate they have on that 360 which probably had an 11.75" in converter and your new converter is a 10.75". The factory flexplates were sized to the converter which some 360's did use a larger converter. Now the other problem is that most likely (although not guaranteed) that B&M is neutral balanced which is wrong for a 360.

What corrects both of these problems is a B&M flexplate everyone is talking about. Either number will work in your case, one is drilled for both 11.75 and 10.75 converters and the other is only for the 10.75 converters but clears the starter better on 904s. You could get the converter externally balanced but then you still have the wrong size flexplate. Just buy the B&M one and be done.