early to mid-May, should be okay, right?
Yes, it should be fine. Saw little snow when I passed through last week.
South face, from the 317, end of April 25

North face, view from the 317, southern ascent of Tizi n"Aït Imi.

Which side is the most practical for logistics, please? I’ll hire a muleteer/cook.
North, as Groschat said, for logistics.
But the southern approach is gentler.
A well-regarded itinerary from a trekking site:
North-South Traverse of M’goun Program
Day 1: Transfer from Marrakech – Ait Bougmez Valley – Ikkis N’Arous (2,200m)
Transfer from Marrakech via the town of Azilal, the gateway to the High Atlas, before arriving at the village of Agouti, the first village in the happy valley of Ait Bougmez, where we meet our team of muleteers and begin our trek to M’goun, passing through the Berber villages of the Arous Valley. 5 hours by road, 2.5 hours of walking. Night in tents.
Day 2: Ikkis N’Arous (2,200m) – Tarkeddit Pass (3,450m) – Tarkeddit Plateau (2,900m)
A gentle climb up to Tarkeddit Pass (3,450m). Panoramic view of the vast northern slope of the M’goun Massif and the surrounding mountains. Night in tents on the Tarkeddit Plateau, a region frequented by nomads with their herds.
Day 3: Tarkaddit (2,900m) – Ascent of M’goun (4,068m) – Descent on the southern slope of M’goun (2,800m)
A long 8-hour hike to reach the summit of M’goun at 4,068m. From the top, a panoramic view of the Central High Atlas range, the Dadès Valley, Djebel Saghro, and the Saharan expanses. 9 hours of walking. Descent on the southern slope of the Atlas. Night in tents at Ifri N’Ait Hamou (2,800m).
Day 4: Tichki Valley – Ameskar (2,100m)
We’re on the southern slope of the Atlas, where nomads come with their herds (goats, sheep, dromedaries). Descent through the Tichki Valley to the village of Ameskar, passing through small villages built of rammed earth. 7 hours of walking. Night in tents.
Day 5: Ameskar – Amjgag Gorges – Valley of Roses – Boutaghrar (1,850m)
A relaxed day descending through a valley of oleander (plan to cross the gorges in sandals), then passing through the village of Amjgag with its beautiful kasbahs. Lunch will be prepared by our cook by the river near the village of El Hot. After 2.5 hours of walking through rose fields, we reach the village of Boutaghrar. End of our M’goun trek. Night in a guesthouse with locals. 7 hours of walking.
Day 6: Boutaghrar – Ouarzazate – Return to Marrakech via the Dadès Valley