I hate it when the website software logs me out without notice while I'm typing a lengthy reply.
I think your approach will be fine. Run it at the slowest possible speed, that's where binding will be the most obvious. Howling is more likely to be from the vertical shaft that needs oiling. I'd do that before setting the backlash.
This setup was used on most of the "Stylist" series machines. Singer never did a good job of explaining the maintenance.
It's important to keep SMO and petroleum products off of that gear. Over time they will deteriorate the nylon, causing premature shrinkage and cracking. Only use synthetic grease on it and the nearby gears.
But the vertical shaft bushing DOES need to be oiled... it makes an unnerving howling/groaning noise when really dry!