purging carboy with baking soda and vinegar?

I don't know if your technique will work or not, but it sounds like you have an idea of basic chemistry. i've brewed a few Berliners. I've never done a sour mash, but I understand they can smell nasty. Purging the o2 from a carboy isn't necessary. You could go the easy route and pitch lacto bugs or a mix of lacto and brett, then after a day or two pitch yeast.

 

As a recommendation, if you didn't, you should try covering the top of your mash with plastic wrap. This can help promote more anaerobic activity during your sour mash. As that vomit smell was butyric acid produced by Clostridium. Some say it can be driven off with a vigorous enough boil. As far as purging goes why not just pitch with some saccharomyces? The sour mash is produces the lactic acid you are looking for already.

 

I think that might just be how a sour mash smells. I have done one or two in growlers with the tin foil on the top. I doubt they had all that much oxygen in them. They did however smell like 3 day old garbage. I tossed them due to the smell but then read that that is just what it smells like.

 

The boil doesn't drive it off, that's for sure. I did one that had the baby diaper and vomit smell, boiled for 2.25 hours, and it was still there, coming out the airlock. I can still faintly pick it up in the aroma in the glass as well almost a year later.

A sour mash done correctly should not smell like anything accept Greek yogurt, nice, clean, tart. The key is keeping all of the oxygen out and having the pH and temp set to Lacto and not any other bugs, or pitching Lacto into a shortly boiled and cooled wort for a few days, then returning to a boil and proceeding from there.