Well actually the bolt together type stands are "more rigid"/less tippy because of the wider spread of the legs.I looked extensively at the bench-grinder and tool stands. The heavy cast pedestal type should be more rigid than the bolted-together four-legged stands, but all of them are too short. Maybe they're ok if you sit down when you're reloading. I always stand.
And far as the height of the stand, a simple/cheap wooden riser can bring the press up to the proper "standing to load height".
I know because I've actually used both type of stands, and continue to use a "bolt-together four-legged stand" with a riser.
https://www.harborfreight.com/universal-bench-grinder-stand-3184.html
No speculation here,