As described, it's akin to finding a purple unicorn 
That said, I would also separate them intentionally so you maximize the quality of everything involved in the entire equation. This is budget dependent, obviously- something which would be helpful if you provided a rough figure 
I have specked out a system with similar requirements previously, but the client had a relatively large budget (and multimedia space). The pinnacles of the system included a 5K? lumens Panasonic laser projector, 80" Panasonic commercial LED display with whiteboard capabilities/built in miracast options to allow up to 12 or 16 mobile devices to connect simultaneously and stream directly to this LED display via Android or iOS apps. Because that part required an app install/fussy details, we also opted to include an HDMI wireless dongle device/transmitter sourced from Amazon. With that device the mobile platform did not matter since all that was required was HDMI output (or display port with an adapter). So most newer laptops would all work fine sending video to the projector. Audio was handled either by the device sending along the video, or using decent (Audioengine?) powered externals connected to the projector. I believe there was also a matrix 8x2 HDMI switch somewhere in there as well before the projector's HDMI input port, etc.
I believe the client ultimately added a standalone whiteboard system purchase used from a school system that was upgrading to something newer. Probably because it more closely resembles a standard shaped writing (wall) surface and did not require staring at a widescreen HDTV to use.
Questions? Go ahead and ask but your requirements for using this device will mostly likely be different enough to make your task even harder w/o some sort of compromise. Budget permits quite a lot more, clearly. This was a $20K+ install.