I can tell you beyond a shadow of a doubt any ferment in a glass jar tossed in the fridge improves a little more over time. Ive got kimchi over a year old that is phenomenal. Some of my best sauces are pushing a year plus in bottles or Mason jars. Oak aged barrels are surely excellent. BliS Blast is a rocking barrel aged sauce but they are not just any old barrels either.
I do my initial ferment at room temp. Finish in the fridge. Add other stuff like vinegar when processing and let it age another week in the fridge. Once you hit 3.6pH or lower the lacto activity goes way down. Its not gunna pop a Mason jar in the fridge if the pH is low enough.
Then pasteurize, strain if needed and bottle. Fermentation will cease but the sauce may continue to improve depending on the length of actual ferment.