I type in bold for anyone with a username like yours; I have the same problem as well.
What type of piping.....and how much more are they saying the cost will be?
Most if not all times running those water lines close to the heat runs allows the ability to chicken bracket and soffett the mechanicals and it is a done deal.
Tell them you'll cross block the joists wherever you want them tucked in and that should provide the same ability to hang them, just like off the bottom.
There is more work involved, not much though.