variable bit rate potentially 40960 x 35 cameras = 1433Mbps potential bandwidth required.
Can you set a constant bit rate of 4096 ( Note this is 10x less than you quoted ) in each camera and see if it stabilizes. 4096 x 35 cameras = 143.3 Mbps well within the capabilities of the NVR
Keep other settings as is.
As others have mentioned the power provided by the switch could be an issue. Ball park figure
5w per camera x 35 cameras = 175 watts across the number of POE switches your using.
I took the 40960 bit rate as a typo. That would be really difficult for any camera to maintain unless built for it, especially an Amcrest at the budget end of things.
Keep in mind that bandwidth is for total usage - you have X bandwidth coming in from the cameras and Y bandwidth going out for anyone accessing the cameras, so that bandwidth is usually the bottleneck. If you consume the entire bandwidth getting data in, then there is no room for data going out.
While I was thinking same my camera settings page for the 5442's allows me to set a CBR of 20480. As they are 4mp i was thinking the 8mp amcrest mentioned might allow double that hence 40960.
This could be a result of the chasing mega pixels scenario often mentioned on here.
This might be one time where a hands on service call might be a good idea. I'm thinkin fo rmyself It would be less physical work to swap out the NVR, So an Amcrest would play nicer with the Cameras. But there seems to be a lot of moving parts to which some info isnt clear to us..... Like camera model #'s and the current settings in each camera.
I'd probably recommend a local tech look at it....and get back to us....
Sounds like the house was completely built onsite and the customers were ready to move in before any building permits were obtained and the foundation poured.... In other words, that large of a system should have been engineered and system integrated by a professional, long before anything was purchased. But instead, mismatched parts were purchased, probably based on price & availability and the system cobbled together, in hopes it might work right out of the box. I realize the OP was handed this mess and now heat is being applied by "upper management" to make it work. I would have told them "Not my circus, not my monkeys". Especially if this is a volunteer position. Good luck to you. Try to talk them into contracting a professional to sort this one out.