I mean, I couldn't tell you the exact reasons for it, but just use a volume calculator. The main reason is likely because the bowl has a lot of unused space, being round, so it takes up more area than a rectangular tank. But it checks out if you just use a simple volume calculator.
Might be on the pricey side, and not necessarily easy for you to get to, but I just saw that House of Fins has some.
It’s a really nice LFS, but it’s wayyyyy overpriced. Depends how badly you want them, I guess.
I only have good things to say about Salgado Aquatics. Juan and Cynthia are great, local delivery is awesome to have, and prices are reasonable. Can't wait to go back!
I was having this problem, too. Same doser. What worked for me was adding check valves. They don’t allow the liquid to flow backwards, allowing in air.
Water has almost none of the beneficial bacteria in it. You want media, or rocks.
I’m not really sure about dipping live rock, unfortunately. It may kill the bacteria. Sorry. Can’t hurt to try, though. Worst case you just have more rock in the new tank.