A big floaty board will support you better when there's not much push to a wave. Conversely, a board with less volume will start sinking if all you're doing is standing there. This might be if the waves are really tiny or if you've gone too far away from where the power is in the wave (aka the curl, the pocket etc). In certain conditions, mostly poor quality windswell with onshore winds (blowing from the sea to the land), you'll find that waves peak up quite nicely but don't have any real shoulder to them, leaving you with nowhere to go.
With your level of experience (or lack of it) bad technique and foot position are probably going to come into play. So yes, if you wait until you're in the trough of the wave before getting to your feet, then you'll be going too slowly - where your bigger board might have let you get away with this, the comparatively smaller 7'6 might not.
And yes, your feet are probably all over the place from one wave to the next. But look, this is surfing, it isn't easy. Go in lots, catch as many waves as you can and experiment. Forget about the rights and the wrongs (other than proper surf etiquette - make sure you know that) and just play around with different things. Find out for yourself the effect of moving your back foot forwards or backwards, angled v straight take-offs etc etc. As long as you're catching loads of waves it really doesn't matter if you mess a few up every session. Set yourself a minimum waves per session (more than 20) and don't get out until you catch them. If you're keen you could do some surf specific on-land training, but if you're in the water loads you shouldn't really need to.