Thanks for that Jarrad. For a use-it-but-don't-collect-it mower, which is probably all this one can ever be now that its authenticity is lost, repairing the rail can probably be done with only modest distortion using the technique you have described. The key seems to be in four points: start from the middle, weld less than 1/4" in each stitch, let it cool properly between stitches, and make each successive stitch at a point diagonally opposite from the previous one, on the plate you are welding in. When I was a kid a good tradesman welder boxed in my car chassis that way to increase its torsional rigidity. Laying it on flat concrete before and after, it only twisted about 1.5" on a diagonal across the complete chassis. However it was a long job, doing it that way. (On that vastly larger car chassis, he used 1" long stitches, and left 1" gaps between them, to minimise heat input.) In the case of the mower frame you can watch the twist after each stitch, and use feeler gauges to measure it under the corners of the frame on a flat bed plate, if you want to get the bad news progressively instead of all at once at the end.
Thank you for the information that you have a deep-tank original engine on your SB45. That seems to make it highly probable that Steve's SB45 still has its original engine, and is a fairly original mower under its disguise.