Portable and compact are different things. Portable means you can easily move it around. It sounds like the issue the OP is describing doesn't have to do with portability, but more like stowability -- the ability to stow it away without taking up space. Going anywhere with it wasn't described. So I'm not sure I understand the issue accurately yet.
For portability, the Benchrest presses take the cake. They're designed to be hauled to the range and used primarily there. They don't need a bench at all. I think Hood were the original, but Harrells makes a copy and Hood brand presses are made by somebody else now. There's a few at Bruno Shooters Supply.
Another unique option is a Hollywood or RCBS Summit mounted on a 5-gallon bullet. It stows in the bucket.
For stowability, it's already been mentionde to mount the press, even an existing Rock Chucker to a metal plate or sheet of plywood and simply clamp that to the edge of a multi-purpose worksurface when needed, and unclamp it and stow it in a box when not.
I recently bought some Plano Sportsmans Trunks at Lowes. They're affordable (compared to a Pelican case or even an Action Packer) and they seem pretty durable (compared to Sterilite or store-brand boxes) and secure (compared to Rubbermaid Roughneck tubs). MTM ammo crates in various sizes are also decent for stowing stuff.
I mounted a press on a steel pipe flange with a piece of 3" steel pipe for a stand. I ended up bolting it to a concrete slab but before I did that I tried moveable bases -- a large truck brake disc, 2'x2' sheet of plywood, truck wheel. They all worked fine for seating, but none were stable enough for resizing. Bolted to the slab with four 3/8" bolts, it doesn't move much, but it does vibrate. I might try some kind of isolation pad between the press and the flange. In any event, it takes up absolute minimal floor space and whatever bench or worksurface I keep nearby does not have to be dedicated to reloading or necessarily have any reloading equipment on it. So while it's not portable at all, it is minimalist in a way.