Compressor does have different settings for upscale method, so you can test with a short clip and see what looks the best,
Set the Resize filter to 'best (Statistical Prediction)' for the highest quality.
You'll not get perfectly clean upscaling from HD to 4K with Compressor. It will do it, but not very cleanly. Also depends on how much action/movement is in the content. Run a short test and see what you get. I'll post some side by side examples later when I'm back in may office.
Setting the data rate to custom should allow you to type in whatever data rate you want.
If this isn't working for you, maybe you have a glitch, or aren't starting with the 'QuickTime Movie' preset. (the MPEG-4 limits the bitrate for some reason)
Plus I kind of assumed since the OP was referring to a logo, that they would use ProRes.