Have you tried use an iron on stabilizer. Use a ball point needle.

here is an article from emblibrary that tells you how to embroider on different fabrics

Use a Fusible No Show Mesh Cut Away stabilier fused to the back of the shirt where the design will be.
If the design has lots of stitches use 2 layers of the fusible No Show Mesh in a criss cross fashion like this - +- . one up and down, one across the first layer.
Use a ballpoint needle.

You could also try using of strips of Shelf LINER ahered to the bottom of your inner hoop with Wonder Tape which is a 2 sided, water soluble tape.
Here is a link showing how to put the Tape and Shelf liner on your hoop.

the strips of shelf liner will hold the shirt taut/tight in the hoop for you while you hoop and while you stitch. It also prevents stretching of the shirt when you hoop it.

This works for any fabric and is great for slippery fabrics or light weight fabrics.

Use the Fusible No Show Mesh stabilizer on the back of the shirt then hoop with the stips of shelf liner on your hoop to hold it tight.

Here is the link below.
You can click each picture to see a close up look at each so you can see where to put the tape and strips of shelf liner.

Thank you for the question and the answers! Live Laugh Download Stitch!

I use the no show fusible mesh in a "patch" where the design will be (more than one if dense). I put water soluble sticky stabilizer in the hoop (stick it right to the inner hoop then put the hoops togethers). Then I stick the shirt and "patch" to the water soluble sticky stabilizer. I also baste the design before sewing (this is where I put a water soluble topper too). If you don't have WSS sticky you can use a different stabilizer in the hoop and use spray glue to stick it down (then baste, etc.).