An external GPU box would work for you, since the offboard GPU would have a full-bandwidth link to the monitor. Depending on which GPU you put in it, though, it would probably be cheaper to buy a new monitor.
That would absolutely be a (albeit very expensive) solution, I didn't even think of that! But that would require Thunderbolt support, which is still a bit rare. And I don't think that would support USB at the same time, right?
They use a Thunderbolt hub (CalDigit TS3 Plus) to a Thunderbolt GPU box. (Razer core X) A single cable goes to the hub, GPU box and all your USB peripherals plug into the hub. The hub itself claims it can run a DP 1.2 monitor, so you could skip the GPU box, if you don't need graphics performance.
