I suspect that if all 4 cameras are perfectly synchronized for time, then you can ingest all photos, from your 4 cameras into one folder, and rename the photos upon ingest (ingest dialog box) using the following tokens:
{hour24}{minute}{second}
To distinguish which camera shot an image, add the {id} token to the above. (the {id} token is the user comment in the camera, so you would have to input in every camera a different comment such as initials, camera1; camera2, etc)
the string will look like this:
{hour24}{minute}{second}{id}
if your cameras shoot several frames per second, Photo Mechanic will automatically append an a;b;c;d... to the end of the file name.
And in the folder, all shots from the 4 cameras will be sorted by name, which is the same as by time, which is what you wanted.
hth, nati