I'm building an advanced flight search website that automatically takes advantage of certain "tricks" like hidden city ticketing as well as choosing the cheapest set of destinations and automatically constructing a schedule, mostly out of personal interest and curiosity. The main issue I seem to be having though is that I can't find any good APIs to search for fares.

I know of the main GDS's, but Sabre's API only seems to permit round-trip searches (which seems very strange?) and Amadeus didn't seem to be interested in working me (I guess because they wouldn't make much/any money off me). For the most part, I'm not interested in building a full OTA with booking, I just need the ability to search for fares like ITA Matrix does. Also, since I'm just a lone developer, I don't have the money to invest in a monthly subscription, but I'm perfectly fine with working off a test API with a limited data set until I'm closer to having a final product, at which point I'd be more willing to pay for a subscription.

Does anyone know of such a service, or how I should approach the GDS's, or what ITA Matrix runs off of?

Don't know about developer APIs, but you could just use Google flight search. https://www.google.com/flights. You can easily issue GET calls with the search terms in the param or using the POST endpoint which takes some sort of request body that looks like it could be reverse engineered in an hour or so.

The GET to the resource looks like:
GET https://www.google.com/flights/#sear...4;q=SFO+to+LAX

and the POST:
POST https://www.google.com/flights/rpc
body:
[,[[,"ss","[,\"502464008F768.A465AA8.1B000DF3\",,6,{\"1\":[[,[\"SFO\"],[\"LAX\"],\"2014-09-13\"],[,[\"LAX\"],[\"SFO\"],\"2014-10-14\"]],\"18\":[[,3,1]]}]","241042555577193",20]],[,[[,"b_al","fa:53"],[,"b_ahr","fa:s"],[,"b_al","fs:133"],[,"b_ahr","fs:s"],[,"b_lr","13:199"],[,"b_lr","5:2"],[,"b_lr","6:76"],[,"b_ar","true"],[,"b_lr","12:0"],[,"b_pe","502464008F768.A465AA8.1B000DF3"],[,"b_qu","0"],[,"b_qc","3"]]]]