Making of the LED plate
I started by measuring everything and by looking at how much space I had for my LEDs. The strip is 10mm wide and can be cut after each 3 LEDs (5cm).
Original lamp is 8mm in diameter and 118mm long. I needed more space plus something to get away heat from the LEDs. I cut a piece of junk aluminium plate 100x50mm and cut out the two ends like this. They fit the lamp socket and help minimizing wiggle of the plate in the socket.
To get the juice to the LEDs I added pieces of clear PMMA to act as a isolator against the base plate.
They have indents on each side to fit into the sockets pins snugly.
LED strip pieces are glued on (self-adhesive). Self adhesive copper tape is used for all the connections. I used lots of kapton tape to isolate pins of the strips and against the base plate.
Connection the the sockets pins: