The 113" kit requires new jugs, pistons, rings, and machining to your cases. Then you need cams, heads, push rods, valve train assem., and if I remember correctly the rocker box has to be machined as well. All this is going to put you over the $4K limit you have.
If you get a Screamin' Eagle Parts catalog and talk to the Service Mgr at your dealer... Find out how far you can go without voiding your warranty. This varies from dealer to dealer. If you can, I'd look at the 'HTCC' CNC heads, different HD cams, 'Perfect Fit' pushrods, and pistons. Does the '06 SE FatBoy come with the high output starter? This would be money well spent, and of course pressure release valves in the heads.
Later. 8-)