I've always been interested in this topic OP...thank you for sharing. I'm in the "not quite retired, but lean FI" category at the moment, so I'm still technically in the accumulation phase of my retirement planning arc.
At some point, I read Edleson's book "Value Averaging." Prior to that, I was solidly in the DCA camp, since that's the industry default, but the idea of VA seemed attractive to me. The main criticism of VA is that market "mean reversion" eats VA's edge over DCA, and I believe this is still the main source of controversy (someone here who is better educated on the subject may have a more informed perspective).
Based on that, for several years, I tried implementing a blended DCA/VA approach (sometimes called "SmartDCA") where I still invested a fixed monthly amount, but instead of peanut-butter spreading my monthly contribution across assets equally with the intent to rebalance down the road, I'd just invest more heavily in underperforming assets to bring my AA as close to my targets as possible with my fixed contribution.
I don't recall (and can't quickly locate) if any source that has studied this method, but maybe others on the forum can help fill in the gaps. Advantages to this approach over either VA or DCA seem to be:
1) No large cash reserves sitting on the sidelines fo VA, subject to the opportunity cost of market growth
2) No rebalancing in the traditional sense (selling winners to buy more losers).
But the effect of rebalancing is somewhat achieved through the process of investing more heavily in the underperformers each month.
I'll wrap up this post with some perspective. I feel extremely blessed to be having this discussion at all. That is, I have assets enough to be on the cusp of FI, and feel VERY fortunate for that, as I'm sure many on this forum would agree. So I'll keep chasing optimal strategy just as you and others, but I'm fairly certain that we all know what a luxury it is to be in a position to be chasing optimal returns vs living hand to mouth

.
I'm reminded of a line in the (underrated) movie "Joe vs The Volcano" in which Lloyd Bridges says to Joe: "
D**ned if I know, kemosabe. All I know is that when you're making those kind of calls, you're in the high country."