Looks good so far.
Photoshop/Illustrator has a feature called "outline stroke" which I've always used for stuff like this. I'd make an object, then set a "stroke-outside" as large as I wanted, then use the "outline stroke" function to turn the stroke into an object (strokes don't scale, which can be both good or bad depending on the context) and then do an merge.
Don't know how to do that in Inkscape or Gimp...

Yup. That's why you save as a photoshop document and save to png right before going to the printers.
FWIW, I tend to save as TIFF, rather than PNG:
1. because TIFF files can store a variety of Photoshop layers
2. because they can contain CMYK and LAB color data, unlike PNG, which doesn't (or at least hasn't for most of my career... things change, I dunno) If I'm going to print I usually convert my images to work in CMYK colorspace while I'm creating them so that I can get a better on-screen representation of the final color output. RGB has a wider color spectrum than CMYK, so images stored in RGB look brighter than can actually be produced with ink.
3. also I tend to work in 16 bit color... which for most people is probably irrelevant, but useful when doing multiple edits to an image with smooth gradients to keep them from looking banded from all the abuse.
For most folks I don't think it makes a hell of a lot of difference. Still sometimes useful to know. PNG is smaller (usually) so I like it for that.