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Here's one statement about the relationship with estradiol, though probably not the whole story:

Progesterone opposes the action of estrogen by decreasing estrogen receptor levels, increasing the metabolism of estrogen to less active metabolites, or blunting the response to estrogen at the cellular level.[R]

Regarding DHT:

Progesterone, which decreases with aging, is a significant inhibitor of 5-alpha reductase. [R]

Based on these statements you might expect that with high enough doses of progesterone you could see some reduction in estradiol and a more significant reduction in DHT. If the idea is to restore balance then it's probably wise to keep everything physiological.