This is a fun topic, we spent 2 years going through this process to find our boat. You have identified 2 requirements as a starting point; now you need to identify the others that are important to you!
Items for thought: ocean crossings (range), steel versus fiberglass, tankage (fresh water, fuel, black water), food storage cold and dry. Single engine versus dual, generator(s) size. Adequate storage for spares in all categories when passage making.
Not many production boats in the 80ft range that come to mind. Now from 55-75' more options become available. It may be you seek a custom or semi-custom boat that was built in a reputable yard.
One challenge is the 10 year mark in the trawler marketplace. There just isn't that many trawlers being built overall. I can't speak to the European marketplace or brands as we limited our search to North America, mainly the US.
Of course one item is budget and ongoing operational costs which may affect the above choices.