Gav, Peter and I paid $80 for a small lot of parts but in saying that I don't think it'll go up by much, if at all, if we had twice as many parts. To a plater I imagine the cost is in the prep as that's the manual component. As long as that part of the job is relatively easy it shouldn't cost a lot.
I wouldn't do everything at once if it's the first time you're using the plater. Try them out with a small collection of parts and if you're happy do the lot.
As for loosing parts, I wouldn't worry too much as long as you don't give them a chance. By that I mean drop them off and pick them up ASAP. I understand your concern there and I'm sure they would as well so bring it up prior to engaging their services. I bet they get that question from restorers all the time.