Based on my professional experience in the automotive field, which is much more economical than the marine field, converting would likely be MUCH more expensive than simply buying the trawler you want.
(My lesser experience in the DIY marine field matches that)
If you are doing it for "fun", then cost and time doesn't matter obviously.
If course you could simply remove the mast.. seal the resulting deck holes and yer done.... But that doesn't seem like a trawler to me.
Edit: looking at your profile it seems you likely know what it may cost..

It all depends on what you want the boat to do. Actual trawling/fishing ? Just a low powered, economical boat ?