Does every full node verify every transaction TWO separate times?
It is an accurate abstraction.

However, the most computationally expensive part of transaction verification is ECDSA signature verification. And the results of verification are cached and reused when they're done a second time. We don't cache the rest of transaction verification as it is subject to many parameters (new softfork rules can have been activated, height, locktime, ...), and it's relatively cheap anyway. We do however cache transaction verification failures.