Thanks for the additional details. I don’t think the setup you described would work in this case with the USB3 HDMI adapter for a couple of reasons;
DisplayLink’s drivers rely on the EDID information from the monitor to describe the resolutions that it is capable of, in the setup you described EDID info would likely not successfully transmit from the TV all the way back to the Win 7 machine, which can cause various display problems.
Also, some computers enforce Windows Media® Digital Rights Management (DRM), which means passing protected content video through a USB port is not possible, and playing video through external monitors connected via USB won’t work. For example, you won’t be able to play Blu-Ray content on your TV via the computer. This would be the same case with any other USB to HDMI adapter as well since it’s a standard set by the computer and not the display adapter driver.
Hopes this helps, sorry for the potential bad news!