Okay, here's the issue. SOP in home canning is that one only works from procedures that have been vetted by a certified food scientist. Certifying a procedure involves more than just eyeballing the recipe and estimating acidity. In the test kitchen, they prepare the formula and test the pH. Here, we're winging it and that's generally discouraged.
For example, Gretchen
notes that these are tomato-based sauces, so they start out acidic.* Well, yes and no. Commercial ketchup is made from tomato paste, and that's considerably less acidic than whole tomatoes. (The first step in making commercial tomato paste is centrifuging, which removes a lot of water and, with it, a lot of acidity.) Now, it's true that ketchup also has vinegar, so that takes up the acidity, but is it enough? When I made my first post, I was skeptical, in part because it is labeled "refrigerate after opening." Indeed, I have known ketchup to ferment occasionally when left at room temperature. Digging around, I finally found a USDA chart
which lists the acidity of ketchup at 3.89 - 3.92, i.e., not quite acidic enough for hot water bath treatment. But, all three BBQ sauce recipes posted so far add even more vinegar. So maybe that's enough. I'd even say probably. I hesitate, though, to say it's beyond question. Which throws me back on that rule that one should only use certified procedures.
* Gretchen also mentions the sugar, and suggests that might have a further preservative effect here. I respectfully disagree. Sugar as such doesn't inhibit bacteria in the way that, say, salt and acidity do. Sugar can only inhibit bacteria if there's enough of it that binds so much water that the bacteria can't find enough to reproduce. Think jam. There's not nearly enough sugar in these recipes, even including that in the ketchup, to get this effect. So, I'm going to concentrate on acidity.
Then, there's another thing. I feel that, when giving folks a present of home canned product, one should be particularly conservative. Plainly, the risk (if any) of hot water processing these sauces would be very, very low. Most people, though, have zero risk tolerance for these things. By way of comparison, I happily use raw and undercooked eggs myself, but when I serve guests a caesar salad, I use a cooked-egg dressing. I consider it respecting that not everyone has my risk tolerance. So, here, I would pressure can.
A final point. Gretchen
said pressure canning would be overkill. Maybe. But, it won't hurt the sauce. I've pressure canned a barbecue-style braising sauce that was definitely low acid. It came out just fine. Not surprising, really, given that (like the sauces we're discussing here) it was a puree of fairly sturdy ingredients. And, after all, commercial barbecue sauces are pressure-canned and they come out fine from a texture point of view. (My complaint with them is that they're too salty and too sweet.)
Please let me be clear. I'm not saying using a hot water bath would be reckless. I'm not even saying it would be wrong. I'm saying it's not what I would do and explaining why. I'll agree it's a subject over which reasonable minds could differ. I would recommend, though, that if you decide to pursue hot water bath processing, you at least contact your local extension office and ask their opinion. If they give it an upcheck, that would be good enough for me.