The bulbs are single pole (S) in this size and the width is unusual.  Nothing is available in an LED with a 20mm "S" base.  I am using two original bulbs that I crushed the glass (in a paper towel + pliers) and carved out the glue to get me a base to work with.

 

Bulbs:  

 LED GY6.35 LED T4 6W Dimmable

 Color Temperature: 4000K

 AC/DC 12V (non-polarity)

 600 Lumens

 18mm OD (stainless bulb bases are 20mm OD and thus you have about 1mm of clearance for the epoxy)

https://www.amazon.com/gp/product/B088TH88JT/ref=ppx_yo_dt_b_asin_title_o02_s00?ie=UTF8&psc=1

 

Glue:

 3M DP270 potting compound black epoxy (about $35.00 in 2020).  Other epoxies would work.  Good heat rating on 3M DP270:

 

Here's the stripped-out bases and the wire that I broke-off is missing on the left side.  I decided to use three strands from some 14AWG wire that I twisted together to make this a stout mount inside.  I am sure 1 wire would have been fine.  These were about 6" long so that I didn't need to fight them to stay in the holes.  You only need about 1.5" to work with. but longer is easier and they get cutoff when finished.:

 

 

Bulbs soldered:

 

 

Here are the bulb pieces taped-up before the epoxy.  I soldered these when the epoxy dried.  Some dripped into the holes and covered the wires, but scraped off easily.  If I had put these on with the bases up, I could have soldered as I glued with a little bit of epoxy run to wipe-up on the tape, but I waited.  Notice the dog-leg jog in the wires because the holes are off-center.  These came out fine.

 

The bulbs finished.  I used a razor blade to cut in at the porcelain and stainless.  Cleaned these up with 95% alcohol to remove the glue residue.

 

Another view of the finished LED: