The three o/us you mentioned all have mechanical triggers which are better when using subgauge tubes.
I'm not sure what you mean by better
. I prefer the more precise pull of inertia triggers over mechanicals. Think of it this way: some energy is required to set-up the second sear. With mechanicals, the energy is captured during the first trigger pull. With inertia triggers, the recoil provides that energy after the trigger is pulled. If you could drop out a Browning or K-80 trigger and compare it to a Perazzi trigger unit, you'd see how many more parts are required to make a mechanical trigger work. I shot mechanical trigger O/Us for 18-years before I went to inertia guns and I'll never go back.
Yes, there is an issue of sub-gauge shells not setting the second trigger of a 12-ga inertia gun. This problem is easily solved by changing the inertia block when you get tubes. I've never had a problem setting the second trigger shooting sub-gauge loads in any of my tubed Perazzis.