Ah. Well as long as the BNC patch bay has 75ohm connectors, you should be ok. (you can tell by looking into the connector, if it has the white shield that surrounds the copper bit in the middle, it’s 50ohm).
everytime you make a patch, you lose some signal level and other nasties. But 4-6 patches should be just fine. I actually have a similar setup in one of our bay’s and it’s fine for HD. Bob could give you a much better technical response, this is just stuff I’ve picked up as the informal engineer at my studio, so it comes with a small grain of salt.