I haven't had success with FIOS negotiations. When my internet-only bill jumped to $80, I called and explained what their competitor (local cable company) was offering, but politely said if you can match it I'll stay with FIOS. Their response was nothing short of "don't let the door hit your ass on the way out"
1 month later I got a "come back" letter with a still-expensive rate with triple play (again, not what I want).
Finally, after 3-4 months, I'm considered a "new" customer and can enter at the intro rate again. I haven't done so yet because the cable company's deal is still active.
Long story short, I think sometimes the best thing is to leave for a few months until you're considered a new customer in Verizon's system, then start at square one.