I don't think drilling it will help cure your problem. Do you know what temp these events are happening or do you just have a gauge with no numbers?
The thermosat is going to open at the same temp. no matter if you have holes drilled in it or not. Small 1/8 inch holes will not flow enough to keep the car from reaching the magic temp at which the thermostat will open. Drilling the holes do help removed trapped air and if that's your problem it will help. I doubt that is your problem because once the system is purged (the first time the stat opens) all the "trapped" air should be gone.
I am not familiar with that particular engine or cooling system but, do they make or will a fast acting thermostat fit? If so that is the way to go. I have had some of the "typical" low cost stats do that to me (drilling didn't help, I tried it). They just don't open on time and can cause heat cycling. I have never had a problem with a high flow fast acting stat. Check to see if Robert Shaw, Mr Gasket, Milidon, makes one that will fit your application. they are about $10 an it is money well spent.