Most of the people I hear supporting rinsing do it because they brew super hoppy beers. Well, since you are dropping $20 on dry hops, seems like you could splurge for a fresh pitch...Not in support of rinsing, but the simple answer to that is don't fear the secondary.
It's not about the money. I think I get my best beer three or more generation in.
There are those (not here so much) that say you will contaminate your beer if you do a secondary, then go on about making starters and rinsing/washing their yeast as if those steps are exempt from contamination.
I don't rinse. I have captured yeast from the conical for a repitch, and have made many a beer using the yeast cake in a carboy.