Unfortunately this forum is lacking in responces and follow up. Did you ever determine what the problem was?
Not that person so don't know, but can give my thoughts on it
I don't think its transmission. Something like transmission pressure I don't think it would do that. In general transmission would be more like switching gears or staying in gear. I feel like saying it happens in gear 1, 2 confuses the situation. People will confuse things when they do this and can go off on lots of wrong things that solve nothing. Its possible to start off in 3rd gear even with automatic (drop to manual shift and use buttons to shift to 3rd and then push on pedal to go AND REMEMBER TO SHIFT BY BUTTONS WHEN NEEDED AND DO NOT DO THIS IN TRAFFIC WHEN FIRST LEARNING IT, but 4th+ won't work here), so try starting off in 3rd gear and see if it still does it? Find stuff like that to narrow down problems.
Could be fuel related. Should use a scan tool and look at fuel trims. If fuel trims are too high either direction then that should show up in how the vehicle runs/moves. I wouldn't be surprised if fuel trims are high here. Then use the rich or lean meaning to narrow down to certain things. Fuel trims really high do throw codes though.
I don't expect it to be electrical. 40+ being fine tells me electrical should be working fine. To me, I wouldn't bother with this.
In theory it could be air related? I don't think its going to be this but fuel trims will express where to look if its this or not. I suppose if the throttle body plate were sticking that might be one of those things that could affect lower speeds by air but it should also show up in idle.
Could be sensor. A sensor or more out of whack but still within values at < 40 could cause major problems without throwing codes.
Really, look at fuel trims when moving slow and go from there. Use something that makes it readily and easily visible so you can glance and see or set to record. Don't do something reckless or drive bad! I nearly always use Torque Pro when test driving and have the phone on a dash holder. Its easily visible and readable at a quick glance for safety.
If fuel trims happened to be good then move along to something else like sensors I guess. As fuel/air would be looking good.
Scan tool can also show fuel pressure and other things with the Sonic.