Timing chain issues

The description sounds like the sprockets are not lined up in relation to each other. Was the kit you used a GM parts kit or someone else's? I have seen this on some of the lower cost parts because they didn't machine them correctly. If it is a GM kit then you will need to check the alignment and check the chain itself to see if it has tight spots in it.

Is it doing it on only one side or both? You replaced the tensioners and shoes or did you use the old ones? Could you maybe shoot a video showing the issue and post it on here, it still sounds like an alignment issue with a sprocket, not a timing issue but more like a sprocket is out of line if you were to look down from on top of the engine, if the chain is riding up on them. Is it only on one or both cams? Are you rotating the engine clockwise when you check the marks? Plugs are out correct?

These are the alignment locations for the stages. Once you have everything in place and the tensioners installed you should be able to rotate the engine clockwise as the tensioners are on the slack side.

That definitely isn't correct. It almost looks like the chain and sprocket are not the same pitch. Where did you get the parts from?

It may be the correct part number but not the best quality parts. With the way the parts have been going it's hard to trust any of them anymore. I've seen some of the aftermarket kits replaced in under 10,000 because the parts were very poor quality. I try to only use the newer parts directly from GM on the 3.6 because they have updated them a few times. The current GM kit number is 12700436.

What are the tensioners doing when you move the crankshaft? With the pins pulled they should apply tension to the chain and seat the teeth into the sprocket. Also if you try to rotate the cam with the chain off is it free to move some? This engine was running okay prior to this correct? It didn't jump time or break a chain first?

What was the reason for the repair? Timing codes, chain damage? I cannot think of anything that would really cause this issue if the parts are correct unless the tensioner is not holding as it should. When the pin was released it should have ratcheted out and locked. Then once the engine starts oil pressure acts on it and will tighten it as needed. Is it only the tensioner that is moving or are the guides flexing? Did the kit include new tensioners or are you using the old ones? If they are the old ones how did you retract them? If new you may want to take it apart and see if it is assembled correctly. It shouldn't retract easily once it extends.
Using the second image I posted above of the chains in position do they match up with this stage 2 list?

1 - Left Intake Camshaft Position (CMP) Actuator Timing Mark- Circle
2 - Left Intake Secondary Camshaft Timing Drive Chain Timing Link
3 - Left Exhaust Secondary Camshaft Timing Drive Chain Timing Link
4 - Left Exhaust Camshaft Position (CMP) Actuator Timing Mark- Circle
5 - Left Secondary Camshaft Timing Drive Chain
6 - Primary Camshaft Drive Chain Timing Link for the Left Primary Camshaft Intermediate Drive Chain Sprocket
7 - Left Primary Camshaft Intermediate Drive Chain Sprocket Timing Mark for the Primary Camshaft Drive Chain
8 - Left Primary Camshaft Intermediate Drive Chain Sprocket
9 - Left Secondary Camshaft Timing Drive Chain Timing Link for the Left Primary Camshaft Intermediate Drive Chain Sprocket, behind hole in sprocket
10 - Left Primary Camshaft Intermediate Drive Chain Sprocket Timing Window
11 - Primary Camshaft Drive Chain
12 - Primary Camshaft Drive Chain Timing Link for the Crankshaft Sprocket
13 - Crankshaft Sprocket Timing Mark
14 - Crankshaft Sprocket
15 - Right Primary Camshaft Intermediate Drive Chain Sprocket
16 - Primary Camshaft Drive Chain Timing Link for the Right Primary Camshaft Intermediate Drive Chain Sprocket
17 - Right Primary Camshaft Intermediate Drive Chain Sprocket Timing Mark for the Primary Camshaft Drive Chain
18 - Right Primary Camshaft Intermediate Drive Chain Sprocket Timing Mark/Window for the Right Secondary Camshaft Timing Drive Chain
19 - Right Secondary Camshaft Timing Drive Chain Timing Link for the Right Primary Camshaft Intermediate Drive Chain Sprocket
20 - Right Secondary Camshaft Timing Drive Chain
21 - Right Exhaust Camshaft Position (CMP) Actuator Timing Mark- Triangle
22 - Right Exhaust Secondary Camshaft Timing Drive Chain Timing Link
23 - Right Intake Secondary Camshaft Timing Drive Chain Timing Link
24 - Right Intake Camshaft Position (CMP) Actuator Timing Mark- Triangle

Also try rotating the engine the other direction and see if the chain stays tight, just to see if there is a different problem. Keep in mind that on this engine you set the chains in position, release the tensioner and then button it up. Rotating the engine to verify timing positions isn't normally done on that engine as the chains are all different and won't line up again. However the tensioner still shouldn't pop in like that.