I don't have one, but you're doing it right if you can't do it yourself. I'd love another but I don't have the tools to shape the plastic end of it, the rest I can handle, and because of that the one I had cracked after little time.
Your best best, watch ebay like a hawk for stupidly low listed BINs specifically for broken/parts only listed Gameboy Advance SP. Look at each one, find one that isn't smart enough to be listed as the 101 by color ID'ing it and being fast on the trigger. Maybe you could get a screen in a busted unit for like $20? (Far better than full price on one even in so-so shape.) The ribbon cable needed is like $10, and you can buy a GBA original for not much money as they're not desirable.
Get the parts, find someone to do the work, better than the BIN pushing crooks on ebay throwing them up there for like $140. I've seen them at open auction usually go for just about $100, which isn't too bad given they had to buy all the parts second hand anyway first, clean them up, do the time consuming work of the shell, basic soldering and screen placement in a clean space to avoid dust/scratches. If you could bag one for no more than $100 I'd do that because saving $20-30 at best buying the parts yourself to pay someone plus shipping both ways won't do you any favors.