As for testing, that would be great. But it turns out that proving anything about human evolution is very hard, because most of the evidence is lost.
As to testing, I suspect we are going to get good at decoding and editing human DNA fairly soon which is going to have a lot to say about these debates. This stuff is either there or not, when and how it showed up (or not) is a separate issue.
EX: Domestic cattle are also around 500 generations old and lactose tolerance has been spreading. http://www.foodbeast.com/news/map-of-milk-consumption-lactos... lactose tolerance: 96% in Sweden, 10% in China.
I don't think new data will help. We know the changes in the human lineage; even if we knew their functional meaning, we cannot conclude whether they are adaptive or not; fixed alleles reveal little about their fixation time, etc.
It could also be due to males having larger brains.
IMO, the point is there are reasonable priors to actually start testing.
Some of these tests may be fairly simple. Do male baby's throw more things than female baby's?
Also, a preference for guns may or may not be there. But, males having more accurate spatial reasoning due to ranged weapons, or hunting, and or fighting seems likely. The obvious alternatives are men developed better spatial reasoning due to very widespread cultural factors seems suspicious. Or women scarified spacial reasoning for some competing features.
Anyway, the important thing is not to debate this stuff it's to actually test it. Until then it's all just hot air.