I think I found Semyonov's "old book"! It wasThis is Sgibnev's Historical Essay of Most Important Events in Kamchatka, 1650-1855, published in 1869. The story there is more or less as follows:
On January 13, 1758 fourier Shakhturov arrived in Nizhnekamchatsk to select Kamchadal girls for the court. He brought to the Kamchatka toyons the Sovereign's order giving the goal of his trip to Kamchatka and the assurance that their daughters would not come to harm. Having chosen six young daughters of toyons, Shakhturov in the same year went with them to St. Petersburg, where he arrived a year later because all the girls had to stop along the road to give birth, thanks to Shakhturov's attention to them.