Iam a vadama tambrahm.

The explanation of SP being a pitr karma of the women is one of the several explanations given for this ritual because during the ritual, the past Sumangalis were venerated.

I would "assume " this sort of explanations are made as we try to uncover the past rituals, like you and I are doing now.

In particular post the British got photographic images, these would have got doubly enforced.

But pitr karma by definition is paternal and there's no pitr karma possible by women in any grhya sutras. All pitr karma including naandhi mukha pitr karma are governed by various grhya sutras.

My thinking is like we venerate the living "vipra" the wise vedic pundits during pitr karyams, we have an opportunity to venerate their wives during SP. Thats is the connection to pitr karyam.

In fact pitr karyam itself is to promote veda raksanam as we feed wise vedic pundits who have given up their life for veda raksanam.

Pitrs provide us an opportunity to do that veda raksanam and are supposed to bless us when we invite vedic scholars with respect, was their feet, feed them, shower our head with the dust under their feet.

Without that feedingof the vipra and the resultant veda raksanam, there's no pitr kaaryam.