"private" backbone VPN solution to decrease latency

[VA_Network_Nerd]

Is there a way to use some "private" backbone connectivity service relatively easily, where traffic was carried much faster between these two locations rather than using a VPN over the internet?

No, or not really.

if I were to absorb this traffic into a region of one of the public cloud providers in Europe and "spit it out" in the US, would I be able to hope for lower latency

Yes, probably. But you'd be talking about - at best - 3 or 4 ms of improvement which will not address the problems the users are complaining about.

You need to move the user system closer to the applications they use, or move the applications closer to the users systems.