Where can one find a current and definitive reference for video quality as it pertains to hosting HTML5 Videos? At my job, I have encoded our sites videos for a couple years by using X-Media Re-encode:
MP4  1024x576 VBR 1500kbps 
WebM 1024x576 CBR 1200kbps

I never had complaints about quality or buffering, I came about with those parameters by trial and error. Now my bosses want 3 qualities, which are:
MP4/WebM 1280x720
MP4/WebM 1920x1280
MP4/WebM 3840x2160

I warned them that the last one (4K) isn't mainstream as AFAIK. They think everyone has iPhone 6 I guess and that tomorrow every device will be Retina capable. I simply need a solid reference I can show my bosses the extra time in downloading, uploading, and encoding 4K will be. I assume the best way to do that is by the numbers (bitrates most importantly), without even considering the other factors such as limitation of broadband/DSL/Wifi, mobile, etc. Thanks in advance.
EDIT
To clarify my question a bit more, my company's server is PostGres RoR S3 to store media, and infrequent use of CloudFront due to our content may need revisions and CF's invalidation process is a deal breaker. So we don't use You-Tube or any third-party platforms as of yet. I'm the front end developer (you probably can tell by the way I described my company's server :P ). So we use HTML5 and a in-house video player we developed. No Flash, no HLS, etc.
What could do is show that Youtube transcodes to 4K at bitrates of ~20 mbps. You can use a tool like youtube-dl to check. Run youtube-dl -F URL So, your upload and download times will increase by a factor of 13-14, compared to the 1.5 mbps stream for 576p that you currently use.

Youtube is best placed in terms of expertise and motivation to minimize bandwidth use i.e. to determine the lowest bitrate that yields acceptable quality.