Does it work when you connect your Surface Pro 4 to your projector using a HDMI cable, (using a Surface mini DisplayPort to HDMI adapter)?
I ask this because if it does then it may work using the Microsoft Wireless Display adapter.
If it doesn't or if it works poorly then perhaps you may have to confirm with Epson whether or not their EB-S31 is HDCP compliant, as it is not stated in the User Guide for the projector.
Here is a quote from the following link that explains it, scroll down to HDCP section on p.2
If a source device is HDCP-coded and is connected to an HDTV display or projector via DVI/HDMI without the proper HDCP decoding mechanism, the picture is relegated to “snow” or, in some cases, a very low 480P resolution. In order to see HDTV with HDCP compliance, both the source and display devices must be equipped with HDMI/DVI connections that can enable HDCP using “software key” decoding
This quote is taken from the Microsoft Wireless Display adapter product page on Amazon.
....Full functionality not available with non HDCP devices......
Hopefully this is of some help.