Hey Nico
Yeah, I know Ladakh a bit. The idea is to do the Zanskar diagonal to avoid the track that winds through the historical paths. Kanji village in the north, not far from Lamayuru to reach Zangla near Padum, then from there, join the Tsarap River and Sarchu on the Leh-Manali road. It's completely off the beaten track.
Quite a few passes at around +/- 5,000m.
I don't know my dates yet, but probably early August.
Your Padum-Darsha project isn't, in my opinion, the best thing to do in the area, and you'll struggle to organize it on the spot. The logistics for hiring a horse man and mules are complicated because locals no longer have mules for their daily needs since the track is now everywhere. It'll cost you an arm and a leg to organize with an agency, and you need to plan ahead.
There will be people in Leh, and you could join a group.
Here's a site with the lowdown and details on treks in Ladakh:
https://www.ju-lehadventure.com/fr/trekking-ladakh/
You can also rent a motorcycle locally and take a trip to the Nubra Valley and toward Tso Moriri or even the Zanskar over several days—great for acclimatizing before starting a trek