MBP '15 unusably slow after being connected to external display via HDMI

I have a mid 2015 MacBook Pro running Mojave that can't seem to handle being plugged into an external monitor via HDMI. It runs fine for about an hour, then starts lagging to the point where it's very difficult to get anything done! I'm at a loss, being hunting around the internet for solutions and have tried several things to no avail.

Resetting PRAM didn't help.

Switching HDMI cables didn't help.

Running things like Onyx and CleanMyMac haven't solved the problem.

I try closing most programs and running only a few spaces, but even just having a browser open with the external display connected seems to be asking too much!

Of course, as soon as I disconnect the external display the MBP runs perfectly fine.

I'd be so grateful to hear if anyone's had a similar experience and what they did to solve the problem. I'd love to be able to use this machine with an external display as that seems to be well within its capabilities.

Thank you!