Hi James, have you found a solution?
I have an old Singer 99K too. It was handed down in my family and I ended up with it because nobody else wanted it. I have used it for lots of projects, and after the motor was greased it is fast and strong enough for my leather projects. With a leather needle it sews two layers of fairly thick hard leather with no problem. Mostly I sew only one layer of the thick hard leather and then use a softer leather that folds around, that sort of gives two or three layers depending on what's needed.
This was originally a hand operated machine bought new in 1933, and then a few years later was fitted with a electrical motor and every thing standard for domestic machines at the time. The motor is old, and probably far from the strongest and I would think a stronger motor would make a big difference in strength. I think there should be stronger motors available made in the 60's and 70's that easily fits this model.
New grease in the motor made a big difference here, I don't know if you have checked this with yours. I like my machine as it is, and hesitate to alter the appearance of it.