Let me attempt to help you feel my pain.
In order of decreasing frequency and severity, these are the problems that I've encountered administering webcasts:
1. (Most frequent and severe) Receiving site lacks a technically capable person who can spare 2-3 hours prior to every webcast to setup.
2. Specialist at receiving site doesn't understand that it takes more time to prepare and setup for the webcast.
3. Receiving site lacks necessary components (missing laptops, missing cables, no patch box).
4. Receiving site's components are faulty (bad network cable, bad hdmi, faulty powerstrip, projector lamp is broken, broken keyboard, etc.) and haven't been tested since the last webcast (usually 6 months beforehand).
5. Receiving site forgets to use wired network.
6. Other minutiae (miscommunicated urls, etc).
The biggest advantage of the chromebox is that I can leave it installed on a TV. Once installed and mounted, it will only be a matter of time before more and more church members learn how to use it (solving 1, 2, 3 and 4).
If a roku would work, I'd use that. The chromebox is the best fit as far as I can tell.