Not so strange:
2-3 Panasonic AG-AC160 Camcorders via SDI @ 1080i 59.94 into ATEM 1M/E without ref =1 frame
1 TVOne 1T-VS-658 Video Scaler for VGA conversion via HDMI @1080i 60 for the powerpoint? If so not an issue.
OUTPUT: 1080i 59.94
ATEM to Extron Component DA might be again one frame
2 Eiki LC-80 projectors (1024x768) Will be scaled down so that takes time again.
If you want to do this right you need to ref the cameras to the atem, then go from the ATEM to a professional projector like a Christie/DP that can take the ATEM signal and can project the image with minimal latency.
My bet is the ATEM actually is the fastest device within your signal path at this moment.
The cameras you use have no genlock input, so they are not the best choice for this sort of a job.