I don't think you need to preheat your cooler with boiling water. If you use hot tap water (whatever the warmest that Comes out of the tap) and let it sit for a bit, I would imagine it preheats it well enough. You can also adjust your equipment temps in Beersmith to reflect the current temp of...
I've started using a 15 gallon pot as a mash tun recently, after using a plastic cooler for years. I also used reflectix wrapped around and secured with Velcro.
Works just fine, however I've had a hard time dialing in strike temps and sometimes maintaining temps if they are low. Raising temps...
10 gallon cooler mash tun, with a 10 inch round false bottom. Works great, never had problem with it. No stuck sparges. 1/2 inch stainless ball valve, needs a nipple. $75 solid.
Going to switch to a bigger tun once this one's sold.
*** edit: willing to ship, buyer pays shipping****
Let it ride. We've all had a brew that takes a bit longer than normal to start fermenting. It usually works out well in the end. See what happens, it'll probably start soon.