I'm open to this idea. I discarded it early on because I thought it would either be too expensive or be too "used" to run cleanly for another 3 years.

Are you suggesting some official refurbishment route or just find them on Craigslist or Ebay?

Swappa. A less shady eBay specifically for phones and like gadgets (though as it gets more popular, we'll see if it stays trustworthy). I've bought three used iPhones and an Apple Watch, never a problem.

I personally wouldn't buy something like this from a classifieds site. But that's because I expect you're just as like to get a cardboard cutout of an iPhone as you are an actual iPhone. If you've used these sites before and are comfortable with them, I'm sure there's options there.

I don't know what it's like in the US, but here (SE Asia) there is a massive market for second-hand smart phones/tablets, usually from places that also do repairs of such devices. Go to any shopping mall in Thailand and (usually on the top floor) there will be dozens of places with devices of varying age.

I don't think Apple's official refurbished stuff will be in the price range you're looking (they only have 7's from what I can see) but I'm sure you can find them somewhere.

I’m not sure you’d like it. I recent upgraded from a 5s with a new battery to a 7.

It was night and day in terms of performance. In particular, Siri works much better.

Developers assume the performance of the latest, so they don’t realize how slow things act on older devices.

I'll second this. I'm still using an iPhone 6s and it works great.

I just checked and there are a couple hundred listed on my local Craigslist for $100-$150.