where would you expect to find the Sun relative to the meridian at noon EST

Neither. Only in rare circumstances would Noon, Solar Zenith and Solar Noon (Meridian) all coincide, or even just 2 of them.

Zenith:

The term zenith is sometimes used to refer to the highest point, way, or level reached by a celestial body on its daily apparent path around a given point of observation.
This sense of the word is often used to describe the position of the Sun ("The sun reached its zenith.."), but to an astronomer, the Sun does not have its own zenith and is at the zenith only if it is directly overhead.
The Sun reaches the observer's zenith when it is 90° above the horizon, and this only happens between the Tropic of Cancer and the Tropic of Capricorn.
Meridian:

In most places on Earth, solar noon does not happen at Noon (1200). The Earth's rotation slowly shifts the meridian experiencing solar noon from east to west. In other words, solar noon happens a little earlier in locations just east of you and a little later in locations west of you.