I have also found great success with Lake Country pads, all flat pads..
The best all-around pad for my Rotary has been the LC Hydro-Tech for the 5" Backing Plate, I have affectionately renamed the Hydro-Shred...
The Cyan (blue) pad is pretty much all I ever need to correct anything with an appropriate for the job compound or polish..
The Hydro-Shreds use a more firm, tight foam that does not absorb product easily, so the product stays on the top of the pad in contact with the paintwork..
This great feature also makes them easier to clean since its just the top of the pad that has the product in it..
And this same pad has the ability to also finish down really nice... It might be all you need to correct and polish LSP ready...
L/C also makes a Tangerine (orange) Hydro that has less correction ability than the Cyan, and sometimes, I will make that second pass after the initial compound pass with the Tangerine and something lighter..
All depends on the zillion variables of paint correction..
The only 1 constant for my needs and process - Rotary Power...
I am sure that these pads can work with other machines, but it will take longer... Remember, its pad rotation that you want to have as much of as possible..
Dan F