BTW, not a great thing to try for the first time on a beer you're brewing for someone's wedding or another important event, in case you over- or undershoot target mash temp by too much. Brew a simple pale ale & make notes on the different ways it effects your process, & decide if it's worth...
I mash in a 5 gallon rubbermaid as well~ holla!
Try preheating your cooler with 1-2 quarts of near-boiling water for a couple of minutes (close it and slosh the hot water around inside), dumping & immediately adding your hot liquor before mashing in. This way your mash temp won't drop as far...