I know what you mean about the sometime similarity of General Schablikine and our "Not Souv d'Un Ami" and have gone down this line of inquiry too.

To date, references to 'Anne Leygues' don't give us a lot of useful botanical detail. It was admired as a free-blooming decorative in Australia and it was an impressive winter bloomer for Alister Clark. The frustratingly sparse descriptions of form and colour suggest a reddish, semi-double rose rather than one that varies widely in fullness and colour like our "Not Souvenir d'un Ami"/ "Huntington Mme de Tartas"/"The rose sold as General Tartas" which I think would be described as pink rather than red.

This rose has a number of quite distinctive features. It is the most sweetly fragrant of any Tea I know, the reverses of the new leaves often show a purplish 'port wine sheen', and the hip is unusually shaped for a Tea - a bit like a pear. The leaflets often do the 'taco' thing - folding up a little from the midrib into a v-profile.
The bloom can be quite dark in colour and have fewer petals in the heat of summer when the blooms look very loose and ragged, while in winter it can produce many-petalled pale coloured blooms. In the milder seasons it tends to be rose pink with suggestions of coral, but it comes in a very wide range of shades of pink.
I have scoured the literature for any roses with all or any of these features and I know you've done the same. Have wondered whether it might be 'Mme Philémon Cochet', 'Goubault', the real 'Comtesse Riza du Parc' and a dozen others.

I'll add a few pics taken here over the years. It doesn't look much like General Schablikine in any of these pics, but gives a range of colour.