If I already had a strong base like yours appears to be, I'd do what I could to adapt the seat I want, for sure. A strong and attractive slip collar could be easily made at a local welding shop that does alum. and SS. Pulling that base out of there and re-drilling for a new base would only weaken the area.
Another thought would be to use the current mounting holes to fasten a thick mounting pad from glass, starboard or aluminum, and then from the underside of the new mounting pad, countersink the studs to mount your new pedestal.
I've always thought that the adjustable base on my salon table would make a great helm seat base. Mine has a very substantial "crank" (Not seen in the photo) that allows easy adjustment to height. Here is one idea for an adjustable base, depending on what your budget is.I was HOPING to get one that adjusts height (the current one is about right at it's lowest, but I would like to go lower) like an office chair.
It sort of looks like there is a slip tube, a seam, that starts a few inches above the foot rest and then extends to the collar with the set screw. If that is the case than could you not simply cut an inch or two from the base of the slip tube.
that base looks pretty bulletproof, if it's ugly why not recover, if it's uncomfortable have a good auto upholstery shop rebuild it and add support to it where needed.
why actually replace it?
HOLLYWOOD