At 50 dollars I think your only alternative is sandpaper. Finding someone who will sell you one sheet of each of the grits you need will be very hard. They typically want to sell the >2500 grits in sleeves costing over 30 dollars. You can buy the 3m combo packs of 1000 1500 2000 and 2500 for about 5 bucks, hard to track down though.
3m polishing sheets will take you to a mirror finish, those packs are about 15 bucks.
so for the 25 dollars for the 3m products then a peice of granite or extremely flat hard surface, or mouse pad if you want a convex edge.
One strop with .25 micron spray would get you to about 60 dollars total spent.
Reprofiling will be difficult but doable. The 1k grit doesn't cut that fast but will eventually get you where you want to be.