Your question: What did Jesus empty Himself of? Philippians 2:7 answers that: He made Himself "of no reputation" (kenoo; laid aside equality with or the form of God). This doesn't say that He emptied Himself of divine attributes; it says He laid aside the form of God...or, in the case that you're presenting, He laid aside equality with God. If you think carefully about the second part of that (laying aside equality), that still doesn't imply that He gave up all divine attributes.
In fact, look at Philippian 2:8 for further clarification: He was found in fashion as a man, and He humbled Himself, and became obedient unto death.
None of these imply a "lessening" or "total absence" of divine attributes, merely a changing of form for a purpose.