A managed switch will work but you'll want to isolate only the specific traffic you want to go to the OT7's and you need to severely limit that traffic. QoS is a network technology that will not "fix" the issue with the OT7 because the issue is with the OT7. It does work however and you can schedule restart events in your managed switches (if they support it) to clear the memory leaks and lag issues.
The way an OT7 works is that is simply receives a message from the OP to connect to the IP video source on an event, or when the camera icon is activated on the OT7 (the URL info is stored locally on the OT7), which also allows it to connect to the IP camera's IP address; the Omnipro has relatively nothing to do with video capability other than the triggered event.
Many servers and PC's have a high-end network interface card that has onboard processing power so removes the difficult task of looking at every network packet from the system's CPU/OS to check packets on the network interface itself leaving more CPU for applications. In the case of the OT7, it is no dedicated network processing capability so it must use it's CPU to read those packets, as well as display the GUI, process video Codecs, and to look to see if the next particular packet is destined for it. On a network with a lot of network traffic, the OT7 gets behind because it is trying to do everything with very limited capability which is why many tablets operate significantly better because they have more processor and advanced or dedicated video processing.
For those that don't understand the technical terms; imagine you are in your car trying to get onto a busy highway that is bumper to bumper and you are looking for your friends car because you have information for him but you also have information you need from all of your other friends that are on the highway which is also crowded with other cars whom you do not know. You have to check every car as it passes to see if it's your friend's car plus you have to manage your own car and figure out when it's safe to get onto the highway while still looking for all of your friends and you are busy constantly painting a picture/video. After a while, without help, you get tired and so... lag in reactions, your paintings don't look so good or you never get to painting another picture, and you missed in checking for your friends' cars. Cars are packets, your friends are the packets destined for you, and help looking for specific cars (packets) is a dedicated network interface card with onboard processing that is missing on the OT7 (due to a couple of dollars it might add to the price).
By limiting the amount of network traffic the OT7 "sees" at it's network interface, the less load it has on it looking at packets and the less likely it is going to get behind. Having a dedicated switch does nothing to help if it can see all the traffic from other switches and traffic unrelated to the OT7. In Pete's case, he substituted a router for a L3 managed switch which worked for him and is a great alternative for those without good network hardware on a busy LAN.
As many have suggested, a tablet works much better. From personal experience, is easier to use also although I have a few OT7's in my own home also. BTW... some customized GUIs and graphics that Leviton shows for the OT7 are NOT possible and simply marketing. Higher resolution is not a capability nor high definition color renderings are possible and some GUI layouts shown are possible at all (and Bitwise OT7 does not provide the same OP functionality). Leviton does not make this tablet, they only sell it. The generic tablet has more features at less than half the price from the same manufacturer with support for PoE plus the Leviton app so may be a future alternative but will still have the same network issues on a high traffic LAN [highway]
Anyway, segregate your traffic, limit packet volume, schedule restarts, and you should have a better experience.