No stainless liner but a clay tile liner in the chimney, correct?I have an identical chimney setup as you and I’m running a BK King with no liner!
It can be risky to make equivalent comparisons with just chimney height. There are several other factors that can make or break good draft. I think it's going to be fine with a 6" liner, but considering that the OP has an existing old stove and chimney, the safest thing might be to measure the draft with instrumentation on the old system.