How do I paraphrase "distribute as evenly as possible"?
Distribute as evenly as possible means "distribute as evenly as (is) possible", in other words, as evenly as one can. It is a comparative construction. The commanded distribution is to be compared with a distribution evincing the greatest evenness that can be.
"evenly possible" makes no sense as possibility is neither even nor uneven, regular or irregular.
Compare:
Jump as far as possible.
Jump far possible ungrammatical