If you have a way to measure voltage and current, looks like it'd be super easy to put a a high power single die LED in there, something like a Nichia, from the high-CRI NVSL219 product line. They're available for around $5 already mounted on star boards. The new XP-G3's are easier to get now in High CRI with a wide range of color temps, though the Nichia's are still easier to get in single quantity pre-mounted on boards.
ETA: The reason I suggested the single emitter swap is because I'm assuming the current LED's are all ran in parallel. I'm assuming a 4.5-5V power supply with the resistor dropping the output to the correct Vf. It'd be better to measure the Voltage at the board at minimum, and the specs from the wall power supply would help to narrow the suggestions even further.