So my idea is to put all the incentives the other way. The tool is designed to operate on a budget of ~$0. I would accept donations, but otherwise have no monetization and therefore no desire to increase "engagement" of any kind. My incentive is such that I actually don't want you to interact with the tool, because that will cost me bandwidth and processing time. I will allow you to have a profile of text and one single image of restricted size, because I don't want to have to host anything else. You will fill out a multiple choice questionnaire with as few questions as I feel I can get away with to ensure at least some level of basic compatibility, and then you do nothing.
Periodically, a cron job will run and see if anyone matches, then it will send you both each others profiles (through good old-fashion email) and ask if you'd like to go on a date. If you've both agreed, there will be a sequence of messages from the system proposing date ideas, locations, and times until consensus is reached. Then it's all up to you. This is designed to ensure that you make a real human connection to the person in a real life interaction before any contact information is ever exchanged.
It probably sounds as though this sort of thing would have a hard time attracting users. I consider that a feature, because it means it'll cost less to run and it will avoid attracting ego-inflation seekers, low effort numbers gamers, and other ungenuine people.
As envisioned, I would expect this sort of thing could cover a moderately sized state on a raspberry pi.