You've hit the nail on the head (from my perspective) and it was basically what I was going to say.

Umami is the big hit on flavour. So replacing with another Umami source. Mushroom ketchup, Marmite/Vegemite, (Vegan) Oyster sauce alternatives would all fit the bill. All of these are shelf stable for a long time, so can be bought in bulk and used repeatedly.