Well, it's not really the cleaning solution, it's the weak device.
I usually use straight white vinegar for the acid content and low odor. Vinegar actually needs no surfactant (soap) because the agitation insures the surface is well wetted but I have added industrial Alconox US detergent powder to no visible effect. You're diluting your vinegar but then adding (at extra cost) the acid of Lemmishine to increase the strength; suspect your final PH is quite near the same as straight vinegar. ??
Yeah, my unit has a heater that helps the acid work a little faster but the major problem is that rationally priced table top units are simply to weak to handle much volume. I can PUT 2-3 hundered .30-06 cases in my tank but it can only CLEAN about 15-20 of 'em! Haven't seen the Hornady unit but, considering the low cost and similar size and weight, I really doubt it's any better than mine.
I used a commercial US in my work many years ago, it was great but it wouldn't have sit on a table top even if I could have lifted the thing! And it cost the company several thousand dollars. Doubt your excellant old dental US cleaner could be replaced for a hundred bucks or less so comparison to what we can afford to buy really isn't valid.
My HF US cleaner has a ditial timer that turns on for a max of 6 minutes, after which the circuitry needs several minutes of cooling. (Again, just a limit on small, cheap US cleaners. ) So, I must allow time for it to 'clean' a small batch for one cycle, then let it cool awhile and clean again, repeating that three or four times, just to clean as few as 20 cases! And then the cases need to be flushed in a soda solution to kill the remaining acid and allowed to dry over night before use. That's NOT my idea of a rational method of cleaning very many cases no matter how purty they look afterwards!
My vib. tumbers handle 150 or so .30-06 at a time with no personal attention. I pull them out when they are as clean as they need to be and they are ready to use immediately. There's no question in my mind which case cleaning method is more practical!