Currently there's a voluntary "if you like us, find us on Patreon". Even being able to provide a "connect to Patreon" button on the screen would be a boost. UX and web site designers are well aware of how many people you lose with each step. Such a button could also auto-switch to the ad-free stream; I once paid for the upgrade but managing the different feed was a pain.
I'm still using Pocket Casts, so it's possible that an integrated app like Stitcher is already doing that. If not, I see a niche that would make it easier for amateurs to scratch out a living. I think the money is there if you make it easy for people to give it.