I'm pretty much in the same boat. I would absolutely hate to fill the whole cargo store with Tritium with mining alone. I'm even too lazy to move with a full tank. That's why I created my low fuel conduct (max 2 full jumps, ~ 145t for my current services per jump or roughly 300t). It usually works like this: One 'blind' jump of ~500Ly, then I grab my DBX and explore/scout forward in a range of the next 500Ly. Once I found a new Tritium source, I order my carrier, wait the 15 minutes, dock and switch to a miner. Rinse and repeat.
And now please, before we all end up in an endless loop of arguing again: Yes, this is definitely slow and in no way competitive to classic exploration. Which it never was meant to be.
If I would want to start from a far point in the galaxy, I would seriously consider to purchase the Tritium before and burn it in several jumps in a row. But that's another topic and not my cup of tea. Possible Tritium shortage in stations is also not on my radar and another topic as well.
But the constant change from mining to exploration and back again in relative short frequencies is definitely my thing.