I, personally, would not use the Twin Jet for anything other than recreational diving. I use them, and I really like them, but they are not for Tek.
I have seen them silt up lakes many times if they are not used properly, and I know this would be an even bigger problem in a cave. The Atomics are stiffer, but stiffer yet, the Twin Speeds, might do the trick.
I have seen an openwater diver have to unplug his low pressure inflator at 60'(big leak), and since he was a little overweighted, panic. He could not swim himself up because of his split fins. I know he made probably 3 mistakes, he should not orally inflatedd, he should not have been overweight, and he should not have panicked. If you were to have a buoyancy failure in a wetsuit deep with doubles, it would be a lot of work to swim all of that gear up with Twin Jets, maybe even impossible.
I also think that, from my personal experience, I would rather wear paddles with doubles just because of the extra power. I also am faster in paddles than Twin Jets (DM swim tests).