I worked at the book/greek store when I was in school all we had were two plain sewing machines. I did the painting not the stiching, but they made tons of shirts using those machines. I can't imagine they were too expensive either b/c our boss was notriously cheap.
They use two or three-ply letters. The first was always the heavy heat adhesive back. They would either put another layer on that in the same fabric (reminded me of a plasticy twill or they would put fabric on it. The most expensive thing we had was the dye machine we used to cut out the block letters.
I always thought they used a zig-zag stitch on them - but I don't know what a satin stitch is.
Of course the store I worked for was sold to a chain of book stores and they no longer carry greek stuff, much less do stitched letters. But, I do know of another store that does it and they do orders from all over the country.
PM if you want the info.