I asked my oma for some advice for you and she wondered if you used starch (spray on) and iron the shirt first and if you use the backing felt on the shirt when you embroider? It's like white felt kinda, and you just sew through it too on the inside of the shirt and cut around it gently when your embroidery is done.
I'd really recommend using a hoop when you embroider.... that way the fabric is taut so it won't dimple like that and your placement will be more centered and crisp.
I do use a hoop, I'm still figuring out how to use it. I'm a slow learner lol
the starch might help... as for placement clues, you may have to make marks on your hoops so you can use simple measurement to get the letters as perfect as possible. clearly you're good with the machine since the threading looks so nice and the larger embroidery turned out really well!
No, I don't use starch or iron and I use the tear away stabilizer