Void Stones?

So I've just about completed my Atlas, have kill the Dark Star and the swampy dude.

I'm getting bored now because I can't really progress / get any more invitations, what am I doing wrong? I doing the maven stuff and tried doing dozens of maps with focus on the Searing Exarch and Eater but nothing?

Also it would be nice to not leave this to RNG if that's the case, why can't I just say, "Yup I'm ready to take on the next boss!" and go? This invitation stuff is tiresome.

You're being a bit vague on what you mean saying you can't progress. Follow the quests on the right side of your screen. Sounds like you have beaten the mini bosses of the searing exarch and eater of worlds. Now you need to put their influence on a tier 16 map to get the invitations to fight the exarch and eater themselves. This will give you 2 of the 4 voidstones for your atlas. These will each give you a 25% chance of a map dropping 1 tier higher and increase the tier of maps on your atlas to T16 (making ~T9-15 maps T16 and T1-T8 higher as well).

Once eater and exarch are dead when you use their influence you get progress toward additional invitations to fight the mini bosses (every 12 maps) and eater and exarch again (every 24 maps).

The final 2 voidstones are acquired by killing maven (follow her questline, capturing map bosses while she is witnessing them (select her icon on the map device)) and do her invitations. These drop crescent splinters and when you have 10 you combine them into a maven's writ that is used to fight her.
The other voidstone is acquired by fighting uber elder which is a bit more involved. you need to fight shaper and regular elder by combining their 4 fragments you get by killing their guardians (shaper and elder respectively). Shaper and Elder each drop 2 of the 4 frags you need to fight uber elder and it is RNG. You could fight shaper 20 times and get the same fragment each time. Use the 4 uber elder frags to fight him and when you kill him you get your final voidstone. This will make ALL of your maps T16 and give 100% chance for your maps to drop 1 tier higher (there are passives in the atlas tree that give you another 100% chance for a higher drop meaning once you have all the stones and these passives, any map that drops is guaranteed to be 2 tiers higher).

Of course you can buy all of these invitations straight from trade if you are in a trade league. Also remember that only maps showing on your atlas can drop. Meaning that when you put in a voidstone you will no longer be able to drop T1 maps naturally (as they are now T4 or so).

Hope this helps.