The only reason you should pay lots for a domain name is if it's hard or impossible to switch. i.e. you're already invested in that brand.
For example, openstreetmap.org is basically "doing to google maps what wikipedia did to encyclopedias". They have been going for years, and have ~ 200,000 users. openstreetmapS.org (not the S) was squatted. They eventually raised funds and bought it. It made sense for them since they had already a lot of brand awareness of "open street map", and it's so easy to add an 's' to the end.
To date I have only bought a single domain ever from someone other than a registrar, usually with a bit of thinking I can come up with one that is not already taken, in your case that might be impossible, hard to judge without more info.
Best of luck with your side project anyway!
If that is the exact domain you want, I'd say $350 is a pretty good price as long as you're serious about the project.