rafezetter
Troll Hunter
I would suggest:
1: Cut off the eroded stub end that's been in the joint with the steel bracket; profile the next - say 50mm to a tight sliding fit in the bracket.
2: Mark where the leg slides through and butts up against the seat base. Drill that out half way through at the same diameter.
3: Offer up the leg to both the bracket AND the seat pan. Check it's tight sliding fit in both.
4: Fox-wedge the top of the leg with a hard [oak, box, teak, meranti etc.] wedge, long enough for the full depth of the insertion.
5: Add slow-set Epoxy to inside of bracket, seat pan, leg stub and wedge.
6; Use mallet to knock it home
Should tighten up quite a bit . . .
Without disrepect to the OP, I think he doesn't have the skillset to even understand some of these instructions let alone DO them (fox wedge?), and yes you'd be amazed at how much of a difference losing an inch off the end would make to the feel and the experience.