I am used to using a cheap intervalometer to capture my time lapses and adjust the camera's exposure settings as the ambient light gets brighter or darker. Since switching to shooting with the Sony A7, however, the camera doesn't allow me to adjust the exposure settings unless their is a gap of around 5 seconds between exposures. Ideally I want to move ISO, or shutter speed with gaps as little as 2 seconds.

Does anyone have any experience of an Intervalometer that doesn't shut you out for this amount of time when using an A7, A7R or A7S?

Are you using the Time Lapse App? If so, there cannot be a exposure change unless if you shoot in Av&AET mode, where all changes are done by the Camera itself, or shooting in M mode and stop the timelapse, restart it after the exposure change.
So i think the best method is using remote control App and tether the Camere to qdslrdashboard... it will get rid of those problems.
Hope this helps