Can I stay in Thailand for 6 continuous months on a METV visa with a USA passport?

You cannot stay for 6 continuous months. You can stay for 60 days, then extend (if you wish) to make it 90, but then you have to leave the country and reenter to reset the counter. To reach 6 months stay, you either exit twice, after 60 and 120 days, or you do it once and you buy two extensions to stay 2 x 90 days. Which is most convenient or cost effective depends on where in the country you stay.

I think people get confused by "valid for". . Which means "valid to use within 6 months, to enter Thailand".

The visa is valid for 6 months from the day it is issued by the embassy. Each time you enter Thailand during that 6 months, you'll be stamped in for 60 days. You can also apply one time each entry for a 30 day extension. Then you would need to leave and enter again to start over with a new 60 day stamp. If you do this 3 times, the final time being right before the expiration date on your visa, you can get about 9 months total in Thailand. But you'll need to leave at least 2 times.