So, a couple months ago, I started using a site for a game I play that provides maps, info on items in the game, current prices for the global market that players can trade on, etc. You can link it to your Patreon account, and if you're a patron for $5/mo, the site gives you historical data on the market, and a few other useful features for the game. There's also a Discord for updates, features requests, general dev stuff, etc, and that's gated (or some channels are at least) behind Patreon as well because Patreon integrates well with Discord, so support and feature requests (through Discord) come from subscribers that are paying.
I mention this because at the current moment, he has 4,757 patrons, and that $5/mo is the only official tier offered. That's $19k/mo, minus Patreon fees. This is the first time I've used a Patreon subscription to power a site account, which I wasn't aware could be done (I subscribe to a few web authors though, so I'm not new to Patreon). I think this is a really interesting way to provide gated site access, and it's fairly low fiction for a lot of people, because they either already use Patreon, or have at least heard of it so it's not some random site charging you or that you are paying. There's lots of benefits I see to this model, and I think if I have a project that fits it in the near future I'll try it myself. Maybe it's something that would work for you (you'd have to set the monthly price at something you think appropriate). $1 from 100 people would get you that $1000 in less than a year, and you might also get better targeted info on what features the people that are willing to pay think are more important.
I agree asking for donations doesn't work. I don't like donating like that. I am willing to allocate a bit of monthly money to people if I feel like I'm getting something worthwhile in return though (it's a limited amount, I try to keep total Patreon expenditure at or below ~$50/mo).