Need some GoPro answers

A gopro has a significantly wider field of view than an iPhone, if possible I'd borrow a gopro first to see if you're happy with the image. In full wide mode at your 8-10m recording distance your priest will only be a few hundred pixels tall on the 4K image showing mostly floor and roof... you can crop in on the image, I believe they call it "virtual lenses", but given this is likely a low light situation the results might not be what you're looking for once you are at iPhone FoV levels.

Audio inside a church will be similar to what the iphone delivers now, if you're happy with that it's all good (assuming the recording location is the same).

As an alternative I'd suggest to spend your budget on a cheap audio recorder, like Zoom F1, and attach that to the PA system. On the used market they should be around 100$, you can run it on USB power using a phone charger avoiding paying for batteries. Then people have a podcast only, true, but really good audio quality without reverb. Being able to listen stress-free to a speech is more important than seeing the person holding it I find.

Yet another idea is to ask your churchgoers if somebody has an Android phone with SD-card slot, then you could buy a micro-sd card and record the video directly onto it. Then it's only about swapping the card, therefore not blocking the phone for anyone. Or use the budget for the gopro for a used iPhone?

An alternative to a wireless microphone, is hooking up a wireless audio transmitter to the PA and feed that to your videocamera/phone giving the best of both worlds at a similar pricepoint (given you found the Android phone owner). Maybe the wireless audio device you mentioned can already do that.

Theoretically for a few hundred bucks, which is the price for a gopro, there should be 6+ year old APS-C or MFT cameras on the used market. They are often sold including the kit-lens. The hard part here will be finding one that doesn't have 30min recording limit (or can be hacked to have none like Sony A6000, A6300, A6500 or Canon with magic lantern firmware). The US model of the Panasonic GH4 has no recording time limit and should be in your budget nowadays.