I've often suggested going directly to a hydro shop when one has a lot of tanks, or when a good dive shop is not handy, but recently I've begun to have some reservations about how wise this is with old bad alloy aluminum tanks.
The problem is, many hydro shop employees have inadequate or only informal training. While the hydro is supposed to include a visual, this is often just a quick peek inside to look for obvious problems rather than a full visual inspection to scuba standards. I was surprised last fall, when I took a couple old alu tanks to our local hydro shop, to find that they had never heard of the neck cracking problem, and were doing nothing to inspect for neck cracks!
This doesn't mean one shouldn't take 6351 tanks directly to a hydro shop, just that if one does, one should have clear understanding of whether the shop is aware of the problem, and whether they will be checking for it. If they aren't, one should be sure after they hydro to either inspect the tanks oneself, if one is qualified to do so, or take them to a good diveshop for a proper visual.
This is, I should make clear, mostly a problem with small hydro shops that do very little scuba business.
