I'm a U.S. passport holder and would like to fly to Thailand and stay for 5 days, then fly to Singapore and stay 3 days, then fly back to Thailand and stay 50 days then fly back to the U.S.

I know the double entry tourist visa will work for this. However, is it possible to purchase only a single entry visa and "elect" to use the 30 day visa exempt at my first entry in Thailand, then use the single entry visa for my second entry? That is, at immigration can I ask them not to stamp "used" on the tourist visa sticker in my passport on the first entry and request a 30 day visa exempt instead? Can I even make that election? I just want to save a little money buying a single entry instead of a double entry tourist visa.

It would be entirely up to the immigration officer on entry. Some might let you get a exempt entry while others will not.

It would be best to get a 2 entry visa so you don't have to worry about it.