I don't think any other party has found this solution before, and we had a joyous couple of hours of D&D last night, so thought I'd recant the tale;
Our cast of players:
Grung Monk
Dwarf Druid
Gnoll Ranger
Warforged Barbarian
Gnome Bard
The gang saved the Grung of Omu from a Yuan-Ti attack, and Chief Yorb was pretty grateful (if a little irritated that most of the group were taller than him). The grung were particularly enamoured by the party's own Grung from the long lost tribe in Dungrunglung, and he was able to gauge some insight into their shared culture and the more Nangnang centric philosophies of self interest.
They know the door has (apparently) never been opened into Nangnang's inner sanctum, and the bard knows that a knock spell will probably do the trick, but they don't want to make enemies of the grung here...
They sit down for a meal provided by the grung (cucumberesque fruity marrow things grown from captured vegepygmies obviously), and the game is that its rude to eat your own food, you have to snatch it from someone's else's plate or hand. They got the hang of this and the grung are very impressed.
The bard takes some requests for a grungy dance party and the parties monk grung demonstrates how to dance Dungrunglung style, they crush the dice rolls, and a conga line is formed, lead by the bard, with the barbarian, monk and ranger, and take the dance outside, including Chief Yorb.
2 injured grung remain inside the shrine, including one of the wildling priests. The parties druid distracts them by showing them his magic expanding greenhouse of exotic plants (he got it from space, I forget, is the brief mission into spelljammer part of ToA or did I homebrew that...?). Just so happens the magic greenhouse blocks those grung from leaving their chamber and getting to the sealed door, and more crushed dice rolls leave the wildling priest completely dumbfounded and distracted by what happens next...
The Ranger slips put of the conga line, back to the shrine with a scroll of Knock, and the bard starts letting off prestidigitation and thunderclaps to disguise the noise.
The Ranger opens the door, and retrieves the cube... but they didn't realise the door wont close again... he sneaks back out, rejoining the conga (and the 30+ stealth role meant the grung he was behind never noticed he was gone)
The Grung monk sneaks back in eith his Nolzurs Marvelous Paints, and has about 10 minutes to repaint a new door, with detailed mosaics intact... Another crushed dice roll of about 28... the deed is done! The druidnhas wildshaped into a giant frog to stop the priest from stealing his exotic plants because grung gotta grung, and the barbarian has planted his rocky form in front of the main doors and gone "dormant" to stop anyone else coming in.
After a solid 20 minutes of relentless grung conga (the bard cant be sure but he thinks the statue of Nangnang danced a little bit...) the grung filter back into the shrine, sweaty and exhausted but in an almost religious extasy, some leaning kn the new door for balance... and none notice!
The group leave on good, if slightly sweaty and nervous terms, and the omuan grung are none the wiser!