How far are you from level 25? I grinded a bit this morning for a couple of hours and feel like I barely put a dent. This is literally one of the worst level grinds I have ever experienced and I've grinded out a lot of levels in other games.
I hit 25 last night. If you don't mind being a bit of an asshole you can expedite the process a little. Change your filters to only display hard and above bug missions (or whatever race currently has double XP). Refresh until you find a game where over 3/4ths of the objectives are done, then jump in, finish it to get the double the XP reward, and immediately leave for your ship to find another mostly completed game. If none of those are available, look for a helldive level with at least half of the objectives done. Even if they fail before finishing, you'll still get a lot of XP for the missions that were completed.
Also try your hand joining a bug or cyborg master game in progress, they last about 10-15 minutes and give around 10K XP. Cyborg tank rolls along the ground so fully upgraded mines (to toss into the center of the map), hard hitting airstrikes like thunderer / airstrike or explosive weapons (like the det satchels or EAT rockets) are a good stratagem to bring in to contribute. The bug burrows through the ground, pops up to attack then dives below quite quickly so either quickly deploying airstrikes, explosive weapons, or mechs would be good. If not taking a laser weapon you are also going to want a fully upgraded ammo crate in the mix with both.
Don't be intimidated by the "master" difficulty, as long as least 1 or 2 other players in the game have somewhat competent stratagem selection, and everyone can keep the resurrection chain going, you should be able to grind out a victory. So far I've found them slightly less challenging than helldives. You also get a trophy for beating each of the 3 masters.
If completing the whole mission from the start, I find level 9 double XP missions are a pretty good sweet spot for XP given, less ability to fail objectives (costing you XP), less time taken to complete, and fewer deaths (which means a little bonus XP). If you are trying to grind out XP soloing easy missions by yourself its going to be a horrible, mindnumbing grind.