It should fit perfectly. Push the LEDs until the disc touches the inner reflector. Hold it still and get the compound glue now.
I used some bicomponent glue but any glue with increased consistency should do.
Just make sure it's strong enough since it will be the only thing that holds the bulb in one piece. Fill the space around the legs coming out of the bulb with as much glue it will take.
Wait until the glue hardens. In my case it took 10 min. and I held the LEDs pressed in the whole time. After it hardened, use a permanent marker to write on the base the + and - legs as well as the voltage it will use.