Never found remmina to be laggy but never tried with 3 monitors. Still sounds better than what I had to do when i had to work from home a few years ago. I had to run a windows vm, to log in to citrix at work (didn't work directly in Linux for me then) to then remote desktop into servers and work in emacs there. It was virtualization hell. It worked but oh boy was everything laggy.. Should have gone one deeper and ran my linux on a hypervisor for a true beauty of a setup.