Just my opinion but I'd recommend you avoid subnetting your network, unless you do have a specific reason to do so. Breaking your existing single network into two might be required if it's a matter where you have non-public info to protect (i.e. records with personal data in the main office) but otherwise, that's just adding unnecessary overhead to basic maintenance, essentially creating two networks to manage instead of one.
A more hassle-free option, if your router supports it, is to just set up a 'guest network', which by default is its own, isolated, WiFi network. It's benefit being, a typical 'guest network' has only rudimentary file/printer sharing support and none of it is tied to the main network.
For a better understanding on working with your organization's network, here's a really nice, concise (1 pg) explanation on IP addresses, pay attention especially to the 'Private Addresses' section:
https://www.bleepingcomputer.com/tutorials/ip-addresses-explained/
This Wikipedia page on subnetting is more detailed but is a good read if you do need to split your current LAN up:
https://en.wikipedia.org/wiki/Subnetwork
Also, I wouldn't worry about how many devices you have connected to your router at any given time. Whether your router has one or thirty active IP addresses given out, it's what each of those devices are doing that might be a factor in actually slowing down network traffic overall. Plus since the Internet isn't a factor in this instance, ALL network traffic packets are going to be tied to pretty specific issues. Then it just becomes something you can guestimate at using basic math -- depending on wired or wireless and how old your router is. (i.e. if it's newer than a decade or so, wired transfers will be in the gigabyte or more range, wireless depending on the 802.11 standards it supports) So if you're transferring a video/audio signal from a phone to a TV and there are twenty other devices connected to that same network, if those other twenty devices are essentially idle (especially since Internet access isn't available in this instance) than those twenty other devices are irrelevant, it's just that communication between those two active devices that need to be taken into account.
And before this just turns into a pissing match where we're all just stating opinions as facts, I strongly suggest you install something like Wireshark on a computer, do a scan on your LAN and get some actual, hard data on your own network. Instead of relying on supposition, you'll have real numbers based on real-time analysis of your own network. It's free, well supported with long history (1998), and available for multiple platforms.
https://www.wireshark.org/
https://en.wikipedia.org/wiki/Wireshark
https://www.howtogeek.com/104278/how-to-use-wireshark-to-capture-filter-and-inspect-packets/
But getting back to the original query you posted, at this point I'm wondering if running an Ethernet cable is going to help in this instance. Yes a physical cable is almost always going to be the optimal choice but reading through your StackExchange write-up, there does appear to be some issues involved. If WiFi isn't going to be adequate though, than it does become an issue.
And as a side note, opting for some kind of powerline solution, networking through electrical outlets, was problematic in its intro years but has since evolved to become are very viable option. But there are number of things to take into consideration with powerline networking, this article is a really good read with details on what to look out for:
https://thewirecutter.com/reviews/best-powerline-networking-kit/
As for your church's WiFi overall, try installing this free (and no ads) WiFiAnalyer (Open Source) app.
https://play.google.com/store/apps/details?id=com.vrem.wifianalyzer&hl=en_US+
There's a 'Channel Graph' option that shows a bar graph showing the WiFi networks it detects (both for 2.4GHz and 5GHz). If you do a scan in the same room as where the router is located (to get a baseline measurement) and then another scan standing right next to each TV you can get some numbers on signal strength. By standing next to the TVs, you'll get an approximate idea on just how strong a WiFi signal is reaching each respective TV. Distance will diminish effective coverage range and you'll also get a better idea on whether you should rely on a 2.4GHz band network or 5Ghz. As an example if you're seeing 45dBm in the same room as the router but say 70dBm next to one of the TVs, that 70dBm is pretty marginal. But you really do need to get some actual numbers to make some accurate decisions off of. There are no set rules that apply to every situation. If your church has a metal, angled roof, that may be more beneficial to a 5GHz network over a 2.4GHz one, with the general rule being to the contrary as 2.4GHz wavelength signals travel further than 5GHz. You could get a better WiFi coverage range by relocating the router, or buying a newer, more capable one. But since budget does appear to be a factor and if it does turn out that WiFi just doesn't work out, looking into wired options might be your best solution.
). I had no idea it would be this hard.
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