My guess is it won’t work well even if it physically fits. The reason the 4k is brighter in “best” modes but not “brightest” is that with the new lamp is they don’t have to filter the non-red part of the spectrum down to match the low red output of the 3k bulb. Less filtering means more lumens get through. The “brightest” modes either don’t use filters or it’s only minimal filtering. So even if you put a 4k bulb into your 3k it would still have the “darker” 3k filter. Not only would your picture be just as dark the colour balance would be all screwed up.
Cheers,
Dean