I have no confidence in a pre-ground bedknife being anything like flat and straight after it has been clamped onto a random soleplate without even a clamping jig. Have you looked into the cost of getting the job done professionally? I have the impression that a raw bedknife tends to cost considerably less than $40, from the right workshop.
We generally recommend that people in your position contact a nearby bowls club and talk to the greenkeeper. Make his acquaintance and ask where he has his reels and bedknives sharpened. The greenkeeper is a valuable contact, who can help you in many ways. Whatever you do, don't use a mower repair shop as an intermediary. That doubles the cost while losing you the opportunity to choose the supplier.