Jon,
Remember the Laramie trip from a few years ago when Indy talked about the Chromebook? Well shortly thereafter I got one as a Christmas gift, but in my opinion using this device at the point of care has been very cost effective and practically useful.
But to answer your question above, even though addressed to Jay, as I understand RDP, internet and intranet. My office desktop RDP's to AC in the Cloud via the internet. I access via the intranet (behind the firewall at the office) my office desktop with wifi, by chromebook with 256 encryption the purchased Enterprise version of VNC viewer made for chrome.
I bet there would be an easily affordable way for Jay to do a similar intranet connection via wifi to reduce the delay time as you are describing.
I know this isn't part of the topic but the chromebook is very affordable and easy to replace so as the point of care device really nice, and then no maintenance or changing/upgrading windows every few years.
Nice thing about the cloud, less hardwired computers to maintain by using the chromebook in the exam room as point of care device, plus with the hdmi cord can share all you are doing to turn the EHR into a teaching tool for a very low cost large screen tv if you wanted.