Super Short Statements: Okay to Cut Priors?

[Artifex_Archer]

I'm fairly proud that I'm currently only about 20% over the most restrictive of my SoPs' length requirements. In getting it to that point, though, I've cut references to all of my prior work. My understanding is that a lot of it can get funneled into my CV [a couple of sentences to summarize various publications/conference presentations] and my diversity statement [employment experience, etc.] 

Conventional wisdom, however, says to include a section on your prior research in your statement. Yet conventional wisdom also says not to duplicate material that can be found elsewhere in your file, so conventional wisdom is conventionally unhelpful here.

I'll ask you guys instead: does it seem like a good strategy to move 'what I've done' into the CV and use the SoP for 'what I will do and how I'll do it at University X'?