That sounds like my boat. When I bought it the old radio didn't work. I bought a new radio and pronounced it as functioning when it could pick up my handheld from within the boat. However the next time I sailed away I quickly lost all nearby signals. Turned out my coax was totally busted at the deck connector. If I were smarter I would have checked that before buying the new radio.
So it's possible you have a bad connection to the mast antenna and are just picking up signals through the coax.
I'll cross my fingers that this season, after running all new wires like you, mine actually works.
As another note, check out the Shakespeare solder-less connectors. They were really easy to install.
Shakespeare Centerpin® Gold-Plated PL-259 Connector