Picking up where I left off in the last installment, I was not happy with the protruding top part of the triangular core.  It was just sticking out too much.   With a check ring in place (the thing that conceals the end of the brass sleeve that will be installed), it was very visible below the ring.   I had even pared-back the tips, but I wasn't happy with the look.

I decided to carefully grind it down using a rotary tool.   I used a squeeze clamp on each leg, and clamped each of those clamps to the MFT.  That held the assembly pretty securely.

I probably took an hour with different attachments to blend in that top core pieces.   I felt like I was a lamp dentist.  Luckily, there was minimal collateral damage.  Nothing some sandpaper won't take care of.

With the 3/4" brass sleeve set in place for a test fit, I wasn't too crazy about its proportions.  It looked too thick.  I'll mull over my options, but for now I'll continue as planned.

I purchased a 36" length of all-thread lamp pipe for the project, which would need to be cut down a bit.  I assembled the full length pipe in the lamp so that I could mark the required length.
Here's the underside.  With the driver pocket hollowed out to account for the reduced thickness of the base, I exposed two of the holes that accommodate the brass pins.   The two pins will need about 1/8" trimmed-off to account for their shallower holes.

The pipe is held securely to the top of the base with a check ring, lock washer, and nut.

The pipe extends above the small lampshade shelves and then transitions to a cutaway sleeve nut, which is where the wires from the base will exit.  The small brace shown here will eventually be anchored to the shelves with 1/8" brass pins.  The brace is primarily to keep the lamp pipe centered.  However, it could also be used to slightly spread the staves or pull them together, depending on the placement of the holes on the shelves.  The only reason artificially flexing the staves would be necessary is if the lampshade ends up being too loose or too tight against the stand-offs at the top of the staves.  For this reason, I'm waiting to drill the mounting holes on the staves until after the shade is complete.  I know I could build-in some adjustability to the bracket itself, but that seemed like overkill for an adjustment that would be made once.

Here, the lamp pipe has been trimmed to length, and the sleeve nut installed.  Another section of lamp pipe continues above to support the LED assembly.   The lower LED channel hub will rest on top of the knurled nut, which will allow me to fine tune the height of the LEDs once I see how they appear behind the lampshade.

Up until now, I just had all the LED pigtails wire-nutted together.   This was a good time to clean up the LED wiring and install the DC barrel connector in the lower channel hub.  In hindsight, I should have chained jumpers between adjacent LED strips to reduce the wiring bulk.  But, since it all tucks in behind the channels, it doesn't really matter.  Except in my head.

The female connector is accessible between two of the channels.  The male connector will be installed on the wires coming up from the lamp base.

Now that the wiring path is all worked out, I'm going to switch to a different product.   The narrow lamp all-thread has the appropriate proportions for the staves, but it looks too utilitarian.  I'm going to switch to brass pipe that just has threads at the ends.   It's a specialty product, so I had to order it from a lamp supply.   I also ordered the appropriate sized die because I know I'll need to tweak the length (and threads) of the new pipes. 

While I wait for the new plumbing, I'll tackle the shade.   I need to go pick out some fabric this week.