I wouldn't worry too much about the brightness.
I run my 20" Apple Cinema Display at maximum brightness (about 220 cd/m2), calibrated with the EyeOne Display2. I get a good screen-to-print match with my Epson 2400.
During the day I can open the blinds and carry on working.
At night I use a single Solux lamp, about 1 metre from my prints, and the brightness matches my monitor.
The problem with that is you are introducing a greater chance of glare having a negative effect on the display. With too much ambient light, blacks can get washed out. While your system may work well enough for your needs, a monitor and ambient light at the proper luminance will net you better results overall.
7700K is very cool (blue). Not a problem in itself, but if you're hoping to have the Solux close to the monitor, providing a pool of light to compare prints to screen, then you will find there's a big mismatch in colour temperatures. To work like this you'll need to calibrate to 5000K - you'll get a better screen-to-print match, but increased posterization on the monitor.
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It may make sense to calibrate at 5000K since the ambient light is also 5000K (or close to) but the display and the print are inherently different mediums. The display being a light-emmitting device will render the image more accurately when set to 6500K. At 5000K the display is dimmer and too yellow. Your eyes will automatically adapt between the Kelvin difference when looking from one to another.
The result is I am getting a temp of 7700K. I do not how serious this is but I will try some printer test files to see the result. I also used the LUT - Large setting and all else "native." Unfortunately I have no seperate backlight adjustment so may have to mess about moving my Solux.
That temp reading is from the default color settings of the display? If so, then I'd recommend what Bruce Frasure states in Real World Color Management to set the EyeOne software to 6500K and let it build a profile to compensate. The profile will degrade slightly but that will be a smaller issue than having a display render everything much too cool. My Apple display runs at 7000K and I calibrate it to 6500K with no problem. There is an ever so slight and faint green cast in the shadows of an image but it is within a very small tonal range and since I know of it, I can easily work around it.
Your backlight adjustment is the brightness control in the OSD.