Neither TDMA nor it being digital will affect what antenna works. To an antenna a signal is a signal is a signal. It doesn't matter if it's a signal modulated using AM, FM, TV, digital, garage door tones, dog collar 'electronic fence' signals, or even radar pulse signals, if the antenna is tuned to work effeciently on that frequency it'll work effeciently on it.
What you're probably having is issues with Simulcast Distortion (Simulcast digital distortion - The RadioReference Wiki
) where you're picking up signals from mutiple towers and the signals are mixing together degrading the signal. Often this looks like you're getting too little signal, when in reality you're actually getting too much signal. This is reinforced by your getting a better signal horizontal than you are vertical.
Start by turning on any attenuator your scanner may have to see if that helps. Next try aiming your antenna around the area to see if you can isolate a single tower (it doesn't have to be the closest, only that your antenna can isolate it from all of the others in your desired system). You may also try using an antenna with less gain and/or lower on your tower. You may even have success by pointing your yagi away from the desired system to see if that will help reduce the signal or isolate the towers.