There are very few production trawlers capable of the kind of long range cruising you're are thinking about. The first requirement is a full displacement hull
design like a Krogen, Nordhavn or Willard
. The majority of "trawlers" these days have hard chined semi-displacement hulls or outright planing hulls like the Ranger tugs. With a planing hull
like the Ranger you'll be lucky to get a 400 mile range, not 4,000. With a semi-displacement hull you'll double or triple that but not much more &, bottom line, these are coastal cruisers.
The Krogen 42 that I found on Craigslist is an anomaly in that the typical price for these boats is more than triple this price meaning this is probably a project
. LRCs have to be strongly built high quality boats and there is a corresponding increase in price. To find one under 100k is rare.