Patch edging brother 1043d versus merrow

I am embroidering jet tag type keychains (double sided) and I am trying to use a brother 1043d for the edging but it doesn’t seem to be dense enough.

I’ve tried embroidering on plastic and using basting adhesive to apply cloth so that I can embroider the edge, however it’s tricky to line things up and I don’t really like the idea of adhesive getting in my embroidery machine.

So when making these keychains, can a Brother 1043d get that dense patch edge if I play with the settings enough or would I really need a Merrow machine for that?

Merrow machines are crazy expensive,….

Or does anyone have other ideas for how to go about making these jet tag keychains?

Thanks folks!