I think you might be confusing the term "trawler" with "trawler"
The term "trawler" has been applied to a general style of recreational powerboat loosly designed around some of the attributes of a commercial fishing trawler. So the "trawler" this forum is about is the recreational vessel, not the commercial vessel.
That said, some participants in this forum may have the experience or knowledge you're enquiring about.
If you haven't already done so, you might pose your enquiry to the national commercial fishing organizations. The only one I'm personally aware of is the tuna boat association in San Diego, but I'm sure there are many others. You might want to pick up a copy of the large-format newsmagazine "National Fisherman" which is one of the more popular trade publications in the fishing industry. You may find some of the commercial fishing associations listed in it, or at least a contact who could provide the information.
The kinds of people who would be using nets on the bottom where they could snag on a wreck would be the shrimpers, scallop draggers, and bottom fish operations. People who use nets for tuna and salmon are usually working the upper layer of water. In Puget Sound commerical gillnet fishermen working close to shore sometimes hang up on rocks and the like.
If your enquiries extend beyond the US, there are active scallop and langoustine (aka Norway lobster, a small, spiny, lobster/crayfish sort of creature) fisheries in England and Scotland. I'd be willing to bet that the scallop draggers working the English Channel have snagged on all sorts of things.