Same problem, as I am 6'4".
We bought our Cheoy Lee 40 LRC because it was the most suitable boat of those we found with sufficient headroom. We likedvthe wide side decks, 5'5" height large engine room, and large shower stall,"ascwell as solid build.
We were looking at older boats in good condition, so there were relatively fewer available innour price range.
Newer boats $$$$, like the Selene, Nordhaven, and the like seem to all have good headroom.
We looked at Defever, Grand Banks, Bristol 42 trawler, Thompson Trawler, and many more that I checked online.
The smaller Defevers 40, 41, and the like, seemed to have very small shower stalls, and felt crowded with features.
Thompson trawlers are supposed to have 6'6" headroom, but as many were finished topsides in other yards, we found that was not always the case.
The Bristols we were on seemed more tender / rolly than did our Cheoy Lee, though both are displacement hullsbwith long keels.
Online resources, here inbthe library, and web searches can get you original makers info, which often has headroom listed.
Good luck with your search.