Thank you for your advice, it is much appreciated.
I embroider on towelling a lot and have no trouble. I use wash away on hand towels and either tearaway or even regular interfacing ( dressmakers type) on Bibs. Are you using stretch towelling by any chance? That could be a problem as you might be stretching it as it goes in the hoop and when you take it out it wants to go back to it's original shape. Or your bobbin is a bit tight.
Getting puckers can be caused by several different things: Using too dense designs on a light weight fabric, using stablizers not suited to the fabric and/or the density of the design, poor hooping, and the moon is out of alignment with the sun and earth. When I first started doing ME, I was getting a ton of puckers but eventually I figured out what works best for me and my machine. Sometimes it a process of trial and error. That's why people do a test design stitchout before stitching on something they don't want to mess up. And, that is why people end up owning several different stabilizers so that they can use the right one for each project.
The first thing I'd do is use a heavier tearaway stabilzer and a temporary spray glue, like 505. If the cloth is stretch and tends to move around, try using a sticky tearaway stabilizer.
I use a size 90 titantium embroidery needle for almost everything. If the fabric is thin or fragile, I use a smaller size.
I don't do burp cloths, so hopefully someone who does will add their advice.