Ues - with up to 10% mineral spirits.

I'm sure by now you have already solved this problem...but for anyone else needing the answer, you can thin gel stain with clear glaze medium as long as its the same base (water or oil). I buy mine at Lowe's in the paint department.

General makes a poly gel varnish that would do what is suggested above. It would not necessarily make it easier to apply, though, since the viscosity will remain the same; it would just weaken the color; become more transparent.

That gel stain sets very rapidly is a known issue. On doors, you want to begin with the panels, finish them to your satisfaction, then wipe down any overage onto the stiles and rails before staining them, and then keep any excess stain off the previously-done panels, because fresh stain will re-dissolve the bits you did earlier, and it is very hard to blend it back in.

Casey

When people talk about putting anything over polyurethane,visions of failure come to mind. Even polyurethane doesn't adheare well to cured poly. I lost count of cabinets and wood trim I've seen ruined over the years by people painting over poly. My advice is to follow instructions given on the net to apply finish over poly to a small sample plus raw wood. When things are dry try scratching new finish off both samples. That's usually enough to discourage such undertakings.

" However, it seems as I go along the stain seems to get thick
and then it's hard to keep it from blotching."

Instead of covering the whole door with a thick layer of stain and trying to wipe off the stain before it dries, it's easier to wipe ON thin even layers of stain.

Wet a rag with mineral spirits, wring it out, then dip the rag into the stain and wipe it on ...ending with long smooth passes along the grain of the wood.

To store the stain, put a small amount of mineral spirits as a layer on top of the stain.