Just trying to get a ballpark price, I have a like new Winchester Extreme Weather BACO in very good condition in 7mm WSM. This rifle was shot very little. Shoots great. Thanks.

Probably 8-900

One of the few rifles you can find ammo for...

11 boxes on local shelf, of a total of probably 60 all obscure ammo

There were very few of these actually made. They were the hardest chambering of all the BACO extreme weathers to find. You might be able to get a bit more than expected at auction; but it would take the right buyer.

It depends on where you live. I saw a like new EW last weekend for $699.99.. I damned near bought it, even though it was a WSM.. Listing it online and it would probably sell for $850.00...

BSA, the rifle you saw in WSM, was it a BACO 7WSM?

That’s a gem of a rifle. I know I’d expect to pay near new prices for that cartridge but I’m a weirdo and likes the 7 WSM.

https://www.gunbroker.com/item/889765609

This sold for $700 in under 2 hours.
I’d expect your EW to bring $200-$300 more, minimum.