I'm not going all grain until this summer... Just so ya know
Your other option would be a thermowell through the side and thermometer. A few issues with that are you have the thermowell sticking into your cooler while you're cleaning, and it might be more expensive than sticking to your original plan. (Now you have to buy a thermowell, AND a thermometer) And most thermowells are not very long, and would measure the mash temp at the edge of the grain bed (Not that that's that
big of an issue) Dropping a long probe through the lid should get you right to the middle.
As long as you're not recirculating I would think sticking a thermometer through the lid is going to be the easiest, and the cheapest option to get your mash temp.