Thank you both! I had not been aware of pcbcart and safe-pcb. They are probably both a notch above the very-low-cost Chinese suppliers, both quality and price-wise. safe-pcb quotes €106 for 10 boards (6*16 cm²), and pcbcart $106. The better quality may be worth the extra cost; I do want the surfaces and the silkscreen to look good.
On the other hand, Elecrow's price is really tempting at $42! I had known them, of course, but it had not occurred to me that they would do exotic finishes... The $15 surcharge seems reasonable, and -- different from the other Chinese vendors I have tried -- they don't seem to charge extra for lead-free HASL. (Since the front panels get touched a lot, I would want a lead-free surface there.)
So, thank you for the great suggestions. Time to ponder now whether I want to give Elecrow a try, or go with one of the upper-tier offers...