this is what i want - a randomized study with a sufficient sample size for post-menopausal women:
https://www.tandfonline.com/doi/full/10.1080/01635581.2018.1516789

it took me some time to understand it, though.

this is the takeaway: there were statistically relevant increases of the 2-isomer and of the 2:16 isomer ratio, without any statistically relevant effect on the 16. there were not statistically relevant effects on any other estrogens, but there was a slight decrease in prolactin. so, the 2 went up and the 16 stayed steady, and everything else stayed steady, too, except the prolactin. that means that it is not the case that the 16 was converted into 2 - it is the case that the female body increased production of the 2-isomer. their concern is cancer, so they very specifically want less 16 and more 2. so, from their perspective, the trial failed to convert the 16 into the 2.

but, this article here explains that the 16 is more feminizing than the 2:
https://www.sciencedirect.com/topics/medicine-and-dentistry/2-methoxyestrone

that means i actually don't want that conversion to happen, and am happy it was not observed.

further, to be clear:

Flaxseed intake did not significantly influence circulating levels of estradiol, free estradiol, estrone, or estrone sulfate in our study. This is consistent with other intervention studies assessing serum (32,35,36), plasma (37), or urinary (33) estrogen levels in postmenopausal women, with the exception of a crossover trial reporting statistically significant reductions in serum estradiol and estrone sulfate with 10 g flaxseed/day for 7 weeks (34). The most biologically active estrogens, estradiol, and estrone, have been associated with elevated postmenopausal breast cancer risk (18,19), thus factors decreasing their levels may be protective. In vitro studies have suggested that lignans may decrease estrogen synthesis by inhibiting the aromatase enzyme responsible for converting testosterone and androstenedione to estradiol and estrone, respectively (28,29,60). However, evidence from intervention trials, including ours, provides stronger support for flaxseed’s role in modifying estrogen metabolism (e.g., 2-hydroxylation of estrone) rather than inhibiting estrogen synthesis.

so, it seems like what they're suggesting is that i shouldn't expect the lignans in flaxseed to have any effect on estrogen circulating in my bloodstream at all, and that is at least a start - do no harm. the decrease in prolactin is also fine, as i produce some as a byproduct of the testosterone suppression.

then, if i wouldn't expect an effect on circulating estrogens, might flaxseed help to suppress testosterone production in genetic men?

apparently, yes - flax consumption, in conjunction with low total fat, should cut down testosterone production by more than a half:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2703189/

so, we're adding some flax :)