Should I get a multi-element outdoor antenna and mount it on a
post above the TV? Is that better than amplified single element?

You can induce more voltage above the noise by the use of more
tuned elements in the signal path. The amplified single element
design is of limited help. The amplifier can overcome coaxial losses
but isn't smart enough to be able to amplify the miniscule desired
signal while ignoring the noise.

Your best bet by a large margin is to get any type of antenna outside.
The best being a directional outside antenna array. If you have a long
run of coax then you should use a at the antenna amplifier.