Carbon killer and Sea Foam are great for the carbon build up. But rimfire will deposit lead over time and mixed with carbon it's fairly tenacious. CLR is basically phosphoric acid and also works well for carbon and may get more lead off with the carbon. But for condensed lead over a long time that almost solders itself to the baffles, either hand scraping, mechanical scouring with pins or ultra sonic, or dissolving in the dip are needed eventually.
If you haven't shot it yet, treating virgin stainless steel with silicone oil (DOT 5 brake fluid or buy pure silicone oil on Amazon) makes it harder for anything to stick.
Lead build up is why you want to prevent the buildup on the tube with a brief but frequent tear down. Pushing the baffles out scrapes the tube out. Lots of folks will open up a can while it's still warm at the range and dump into a ziploc bag for brief brushing at home. Ridges of buildup inside the tube make takedown harder and using dip or CLR or pins or ultrasonic on the tube won't hurt the metal but may degrade the paint/finish.
The mount rear cap of the Element is semi-permanently held on with thread locker, and with AAcs baffle pusher you probably don't need to open it up warm at the range.
Realize for years people shot thousands of rounds through sealed rimfire cans and never cleaned them. You could go a few thousand rounds, plug the front cap with a stopper, carefully pour in the dip watching for air bubbles burping, set it for a day or two, carefully pour out and rinse, and take the spent waste acid to your municipal hazmat collection. Lots of people use the dip, but just don't be casual about it. Compared to pin tumbling it's actually more work overall.
Maybe you could find some body to borrow a pin tumbler from every few thousand rounds. Or just scrape off the major crud and rock on.