I've ovulated as late as CD 40. I would never quit testing with opks on CD 16.
Also my bbt is always in 96.6-97 range pre-O and just over 97 post-O so you're not alone in having low temps (though I realize that it's weird when it's a departure from what you had before.)
Get the opks from amazon because they are cheap and individually packaged. Then you won't feel bad using a lot of them per cycle. If you aren't testing twice a day you could also do that (though that burns through them faster).
As for BBTs, this is my opinion -- you don't NEED one that goes to the hundredths place, but you DO need one that is accurate to the tens place. In fact lots of them that go to the hundredths place are not actually accurate to the hundredths place (including Mabis--read the instructions), but they are at least accurate to the tens. And a lot of thermometers that go to the tens place are accurate to something like 3/10s which is not sufficient (needs to be 1/10). If your thermometer is accurate to the tens place then it is ok to see flat line temps, in my mind. If you'r fluctuating from 96.67 to 96.71 you'll see 96.7 over and over. But if the thermometer is in fact accurate it should be able to detect a shift.