You’ve asked, most people are saying the same answer - you might not like it but that is your best bet (obviously none of us have seen it).Thanks for the reply Ben-gee. Unfortunately, the stack is already in place and there is no chance of adding a vent to the roof. Any other ideas?
You say there is no chance of adding a roof vent - there will be, if May not be easy but it will be possible.
But don’t forget, you may be able to vent your drain system more easily elsewhere - get a local plumber to look at it for you.