Just wanted to update this in case the info might be useful for anyone.
The process was actually far less painful than I'd expected. People were telling me to expect to wait at the NY office for 4-5 hours. I waited for exactly 70 minutes. I arrived there at 10:35am. Upon submitting my application, I was told that it could take 24-26 business days for my multiple-entry PRTD application to be processed. Nope. The embassy took exactly one week. I submitted on Wednesday, they received it from the VAC on Thursday, and sent it back to the VAC the following Thursday. I went to pick it up on Friday.