Here's basically the shownotes of the things I've tried between the previous log and this one.

Modelling a new solution

Therefore, I can help you apply to the engineer and redo 1 product number C-CN39 for free.
 - Eleven

This is the response I got when I told Eleven that I couldn't get anything unblocked. 

I thought that I might as well try and tweak things so that there was a better chance of success:

I made sure that the input ports were still aligned:

I wasn't all too eager that the solution became so large, which was extra painful when I found out that Nozzleboss had recently tested out his ultrasmall heatblock:

He's using a relatively small heater cartridge which is like taking a thermistor and adding 0.5mm all-around. It's an UM2 cartridge that is M4 x 16mm, which comes in 25 and 40W configurations.

The engineer got back to me with annotations on where there could still be issues:

After seeing the current WR (world record in Trackmania-speak) and having the experience that longer paths = more powder, I put this strategy on the shelf.

Trying to unblock the solution I already have

This is the stuff I bought:

• M6 x 5mm flat-point stainless steel grub screws
• M6 x 6mm Pneumatic Coupler 2pcs
• 60ml syringes + 5mm PVC tubing 3pcs
• Silicone tube 4mm ID 6mm OD clear 1m

I got the coupler and silicone tube only after I got the syringes and found out that the 5mm PVC wasn't the type of tube that the uni just happened to have. It was still useful though, as I needed to cut a small bit of the PVC tube that would go around the syringe and better grip the silicone tubing:

I'm glad I got the 60ml ones, because I was deciding on the 3 pack of those or 1 singular 200ml one, and I think the latter would've been somewhat unwieldy.

I also had the idea of trying to use the water like a fluid chizel, and noticed my smoothie-bottle of Innocent could be an ideal candidate to hold the syringe in place. Thus, I used a carpenter's knife to cut a (triangular) hole in the bottle and filled it with water to a convenient "fill-line":

Unfortunately, the chizel + mallet idea didn't seem to do anything. The next day, however, there did seem to be some residual powder that seeped out:

Perhaps the issue was air pockets? Thus I tried doing a displacement where I'd put water in a syringe and pull the plunger up to force air to bubble up and be replaced by water:

I then plugged the 4 cardinal-direction channels, wrapped the c8or in foil and did a test boiling. Nothing seemed to come out so I just put the c8or directly into the pot.

Still no results, so on the next attempt, I filled the coaxial8or with water, blocked all input channels, froze it and then heated in an oven to boil off the water.