As Magicotoby pointed out, the reasons have nothing to do with being a monk or community perception for them. Its your Rio vs. the Rio of every other dps out there.
And 2600 is low, compared to other DPS out there. There are tons of DPS that have everything (both Fortified and Tyranical) in 19+ and some in 20/21. You have a few there in 15. Focus on increasing your rio a bit. Do ToT16, 17, 18 ect… And then next week do the same for fortified.
But, the fastest way to do keys is doing your own key. 100% proven method of not waiting more than 10 min.
As for being a WW monk. Utter BS. If you see my Armoury you will see that I run ALL my dungeons with a WW monk. No issues at all.
But TLDR: If you want faster invites and in general a better experience in M+
Here is a long list of improvements you can do: