Sorry I missed the question earlier in the thread. A good source of non-combat XP is making hugely profitable sales, which are recognized as XP events under some criteria. Buying black market weapons and running them to an ongoing conflict (Nortia is probably the eternal one? Haven't gone to look). I'm honestly not sure if there have been significant nerfs to this though, as most of my playtime has been the newer non-combat activity: exploration.
Discovering anything gives you instant XP, as you may have noticed, it's not a huge ton of XP. Surveying also gets you XP. When you go through exploring, reading all the text for clues and finding those well hidden big-hauls (motherships, big derilicts, stations), I found my space archaeologist was leveling up at a good rate.
I should qualify 'good rate' though. There are significantly fewer salvage and exploration relavant skills compared to combat skills. At level 16 I felt like I had everything I needed, and somewhere in the low 20s I had every skill that was remotely relevant. Basically all of the heavy XP requirement in the game that's left for me would involve combat anyway. Might as well have combat provide the XP.