You just bought an i1Pro2 right?
Sounds like a ColorMunki so I don't think measuring the illuminant is going to fly unless there's some software that will save from that device a cxf file and the OP has the software to build profiles with it.
I got a 3500K Solux yesterday and it's certainly warmer than what was there but when I placed a Whibal
under both the 4700 and 3500 and shot them, I was surprised that my .NEF/ACR gray eyedropper balanced it at 3700 (+3 tint)
(and the 3500K bulb came in at 3150).
That test is meaningless, ignore it. You need to measure the actual illuminant. Shooting and viewing the CCT value from a raw converter isn't even close to an accurate or ideal way to gauge what the Solux is producing.
And yes, by and large, this sounds like a big rabbit hole about to be dug. IF you want an illuminant specific profile, you or the person building the profile needs the measurement data from that bulb typically in a format some software and access it for profile creation (a cxf file). You can do that if you get an i1Pro (I don't know if the ColorMunki + software can do that).