For what it's worth, aviation and maritime ops are found in the HF band. Transatlantic flights can be heard by listening to Gander and Shanwick ATC, and oceangoing commercial shipping uses HF frequencies.
But most of that stuff is SSB, so the 350 won't do the job.
I would suggest looking for a used desktop RX, like an Icom R75 or a Drake R8. Or, many if not most Ham HF rigs have general coverage receivers. Nothing wrong with using one of those for listening to HF broadcasters or aviation/maritime/ulility stations. Then, if the bug bites you and you decide to go Ham, you're all set for HF!
It is a simple matter to make a nice wire antenna for HF, so don't assume you have to limit yourself as far as antennas go.