Yup 1.25 is sort of the worst speed imaginable for my system.
I DO have a solution... but oh boy, is it weird.
I probably need to write another blog post on the solution, but I don't know when I'll have time for that.
In the mean time, try picking a move speed that doesn't stutter too bad, or just "deal with it" until I can get the post up.
The fix should slot in pretty easily to any existing tile based collision system, so you shouldn't have to worry about continuing with your project and finishing it later.