Hello sir, my name is Tom, I am streaming engineer with more then 6 years of experience.
I worked on projects such as IP TV platforms, social networks, and smart surveillance systems.
I see that you are struggling with different channel resolutions and that you would like to put them all in same resolution, to do that you must transcode each channel and for number of 250 that you say you have that will be very CPU expensive, to do that you would need 3 dedicated server of approximate price of 3000 USD or alternatively you would need to set up a farm of raspberry pi devices, one pi channel to do the channels transcoding.
In any case this is very interesting project and I would love to assist you.
If you are interested we should meet online and discuss the project details.
Best regards, Tom.