I've been using oils for about 30 years or so. I use Gamblin almost exclusively, sans a few colors. Certain colors (for me) call for a few different brands that I prefer over Gamblin (Winsor-Newton, Daler-Rowney, Sennelier).
I use Liquin mostly for glazing and layering. Rarely, I'll use it now as a "medium" to help the consistency of the paint when it's dry, and do prefer the Gamblin Solvent-free gel these days. I understand what you mean about it having a bit of a shine, but two things: use VERY little of it. And if you're using it with the same color to cover a larger area, make sure you mix it all first so that there are no differences between the surface sheen. That can look icky--I've had that happen, especially when I've used too much of that stuff. It really needs to be used sparingly. I put a dot of it on the palette and pick a tiny bit of that dot up with my brush to mix it with whatever color that I squeezed out of the tube (or am mixing).
When I used to do this with Liquin, I used a tiny drop of stand oil if it got too runny or shiny, and it took that edge off.
I'm a big fan of that gel, however. It was like a solved problem to Liquin for me because of how Liquin dried too shiny and too quickly.
I also use the W&N Underpainting White, but only for underpainting when I plan to layer another color over it and scratch through to reveal the white (or whatever color I mixed it with) from underneath. That's something I've done for many years. Warning about that paint, though; it smells strong and can even give you a headache. It dries super fast, too. I've found that it practically surface dries on the same day, sometimes in a couple of hours, and I lay it on thick.