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Woody does use the mage hand to move the pole back and forth.

Athletics Woody: [1d20] = 7 + guidance [1d4] = 3 = 10

"That was a close one."

With Woody Mage Handing the pole as necessary, both Sue and Jim make the vault across to the north walkway look easy.
Woody looks like he's slipping sideways into the muck flow until Darren calls, "Lean into it! Lean Forwards!" and he does so, just landing in a crumpled heap on the north walkway. "That was a close one."
Darren follows, not as elegantly as the first duo, but with less flailing than Woody.
After carefully climbing up the two foot high slippery stonework adjacent to the actual weir, the party take up their previous marching order:

• Jim (with pole and coin),
  Woody (with map and Direction Stone),
  Sue (with one of many weapons),
  Darren (just shield equipped)

***
After about fifty paces (double steps) the tunnel turns fractionally left and then after another fifty or so paces again turns fractionally left. There is a three and a half, perhaps four foot diameter pipe that angles off to the right. It appears dry, albeit with the lightest covering of lichen.

Woody's Stone shows that the thiry foot wide promary tunnel is heading more westwards than anything. The dry spill pipe heads northwest.
The spill pipe would require crouching or crawling but could be navigated easily enough.

What next?

"Can you get a peek in there with that light?"

Sue will crouch, trying not to use his hands on the floor.

The Mage Hand cn take the coin-light out to thirty foot from Woody and illuninate for a futher twenty foot brightly and then another twenty foot dimly.
It seems to go in a straight line and is unoccupied.
The constantly echoed dripping, burbling and thwopping of the main sewer channel makes it difficult to discern any noise down the quieter side pipe.

***
Sue finds that if he puts away his weapon he can crouch and advance slowly, knees bent, back parallel to the pipe to avoid weaponry smacking off the top of the pipeline.
It's Difficult Terrain but manageable. Small stabbing weapons could be wielded effectively.

"Sue if you want to go in there I can borrow you my magical dagger it does shed light in a 10-foot radius.

Anyone have a couple daggers they don't mind sharing for a bit? Jim asks as he holsters his mace. I'll take point again if this tunnel is our path. Assuming the party agrees, Jim will head into the tunnel, hopefully with a dagger in one hand and a lit coin concealed in his other.

"Jim if you're going first you can borrow my magical dagger."

"I have some normal ones. How many you want?"

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Woody's dagger glows? Does everything we find glow? lol

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The cloth doll didn't glow.
What will Jim do with the coin? And the long pole?

======================
Could Sue hook the pole onto his gear, and drag it?

Sue sees that the hook on the end of the pole has no sharp edges and could be hooked onto something, maybe his weapons belt?

Darren offers to shuffle along carrying the other end after he's unequipped his shield. "We might benefit from one of the others in front and one of them behind us, of course."

One or two will suffice Woody. Thank You. Jim will take one in hand and tuck the other inside his belt to keep a fist free for the coin.

"Woody in the rear is not a great idea. He is soft like a sack of grain"

He sighs. "But we should bring this with making a racket."

"Or hook it onto me and I'll follow Woodsy and you hold the back of the pole and guard the rear?" offers the cleric.