I think you are going to hit a survivability wall as you approach GR50. Possibly damage output as well.
You need that Traveller’s ammy as the Endless Walk set bonus provides damage mitigation as well as attack bonus, which suits the run, then stand and deliver style of the thorns set. You also need the Justice Lantern ring for huge damage mitigation.
Sheet damage does not matter for Invoker - most of your damage comes from thorns, which does not crit based on gear CHC and CHD. To that end, CHC and CHD on gear is unnecessary (both your rings, but I can’t see if you re-rolled sockets on them…). You want to stack CDR instead to more regularly hit your skills, which should be set up for bonus thorns damage. To that end Fury is useless on the Punish skill (as is Roar and Retaliate - making cubed Angel Hair band sub-optimal) and you should be running Consecration/Bed of Nails over Provoke/Too Scared to Run (you should only ever be chasing champs).
Run between champ packs with Steed, hit Akarat’s Champion, Iron Skin, Consecration and watch shit melt. Time that properly with Conv of Elements Physical cycle and you will do stupid, stupid damage.
You are also missing the Crusader Shield Akarat’s Awakening, which reduces cooldown of all skills on block. Under-performs at low GR’s where you kill stuff too quickly for it to proc enough, but it will come into it’s own from GR55 or so.
Running Nem’s with RoRG cubed is fine, but with a Justice Lantern and Compass Rose ring, you will be potentially giving up the Conv of Elements bonus. Good for farming, but may not be good for higher GR’s as your damage output begins to struggle. If you hit that wall, put Conv in cube and put on your Invoker bracers.
As mentioned, Angel Hair Band is going to under-perform in your cubed armour slot as 3 of the Punish runes add direct attack damage which is always going to be crap. The preference is Heart of Iron, which will significantly add effective damage output through boosting thorns.
Hack in the weapon cube is ok, but I am pretty sure it adds thorns damage to your actual attacks only and the bonus remains static, ie unbuffed by skill use. Consider replacing with something like Blood Brother for additional mitigation, depending on where your weaknesses crop up.
Other than that, life on hit is great paired with a quick weapon and high attack speeds. Your sword actually looks pretty good. You could re-roll damage for CDR instead. Or the socket and hit it with a Ramaladni.
Oh, and more Ancient pieces! We could all do with more of those… :)
I am currently running Invoker adhering to most of the above, working my way up the GR levels. GR55 so far in about 7 minutes. Health bar barely moves unless I get a particularly hard hitting champ pack. Think I hit a pot once in that 55, which was the first time in any GR. Should get to GR60/65 without much drama as is.
I really like the thorns set. I played a thorns crusader briefly in season 4 but it was underwhelming and under powered. Blizz stated they were hesitant to buff the Invoker set to competitive levels if it meant gameplay would become static. Thankfully they have managed to avoid that as I find it quite fun and still involving to play.