Is re-wiring an early version of the Polar Express so that it can have constant voltage to the headlight a possiblity? Has someone done a 'how to' video on the subject?
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Three components and the LED will give you what you seek. This circuit drives the LED at the full 20 milliamp rating down to about 3-4 volts AC on the track.
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I used the circuit posted above by @gunrunnerjohn as the basis for a couple new PCB's including my first ever surface mount board.
Here are the results so far.
First up is the version 1.0.1 through hole component PCB. I made a few tweaks to the version 1.0 board shown below.
Diode (1N4003), 100uF Capacitor, and CL2N3 installed. Note: this is actually a version 1.0 board.
LED light test, power is supplied by a seven volt AC output wall wart.
Here is my first ever surface mount PCB. I thought with only three components, how hard can it be?
This picture shows the PCB after the surface mount components are soldered to it.
Diode (Mouser P/N 78-VS-1ENH02-M3/84A)
100uF Capacitor (Mouser P/N 232-35TRV100M8X10.5)
CL2N8-G (Mouser P/N 689-CL2N8-G)
I don't have a hot air station, used my soldering pen, capacitor was the most difficult to solder to PCB. One tab on the cap was rather easy to solder to the board, the other not so much. To get the cap fully seated, I changed the soldering pen tip and heated from other side of board. Actually worked well, was surprised and happy. Will try soldering cap to PCB first if there is a next time. I do have two more blank PCB's.
Successful LED light test of the SMD PCB.
Size comparison of the two boards. Although I made the SMD PCB as small as I dared, it actually cost more than the through hole version. I ordered the SMD version 1.0, the through hole version 1.0.1, and another board I am working on at the same time from Osh Park. Somehow didn't specify 2 ounce copper and thin board for the through hole version or the third board. Felt bad when Osh Park sent the three SMD boards in a separate USPS mailing. Will be more careful next time multiple boards are ordered.
I have a couple hot air stations along with a couple lighted magnifiers in the "Save for Later" section of my Amazon cart. I ordered a different crimping tool yesterday because the one I have isn't for the JST connectors I bought. Maybe I should stop now? Right, like that's going to happen. 
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A tip on your capacitor soldering issues. Many layout programs, including DipTrace that I use, have incorrect footprints for some parts, one instance being some of the round SMT capacitors. It results in the pads being too short and almost totally hidden under the cap. If, as I suspect, you're using the DipTrace pattern FT-6.3mm for your board, it's a part that has this issue.
This was brought to my attention when the PCB assembly house complained that they were having problems soldering the caps, when I researched the issue, the reason was obvious, the library pattern was incorrect.
Here's the library supplied part.
Here's my modified footprint for that cap. Note the longer pads to allow for proper soldering.
