The lowest cost option is taking the seat off, cutting it down to make it narrower, and maybe removing the stock padding and adding thinner gel padding. There is also a Butt Buffer brand seat pad that is very thin and uses hospital bed cover material that prevents bedsores.
To recover the seat, the lowest cost option is to buy a new large T-shirt, preferably one of the dry weaves that handles rain and sweat better, and cutting it to fit then sewing it together under the seat.
I did this type of seat cover a few years ago and it works well, especially since I rarely ride in the rain. You could hire someone to stitch up some vinyl or leather for a better looking and longer lasting cover.