Running parallel stories without every player in every strain is a good idea. Players may take part in one or more strains, depending on their time, and each strain is less vulnerable to individual players being stuck in real life. The constraint is the number of strains the SG can handle.
Bad Apples even ran parallel seasons; three stories per year, different seasons, but in parallel. Any inconsistencies were brushed under the carpet.
If you run an established covenant with lots of covenfolk and lots of activity, it is relatively easy to enforce grog only stories. Your magus wanted to join? Well, he did not even know about it. If the covenant is busy enough, even the Tytalus busy-body cannot keep up, and if the players are difficult, throw out a red heng. Your magus joined the grogs to find the lost goat. You found the goat. Nothing interesting happened. Exsposure 2xp. Then, of course, the other grogs went elsewhere and had a story worth telling.
However, in a fledgling, under-staffed Spring covenant, nothing really goes under the radar, and it may be important for the magi to explore the area too. Barring magi from a story may threaten the suspension of disbelief. Some magi will want to stay behind to study, but some magi are urban and sociable, busybodies, or whatnot; there need to be a reason for them to stay at home to keep the story plausible.
Things may work out better if the magi's downtime activities are narrated in advance, rather than being recorded after the stories are told. Magi might be offered, or even forced into, a story after they have committed the vis for an enchantment. Possibly harsh, but more realistic. In practice I find that most players are constantly behind with their paperwork, and cannot declare their characters action in intervening seasons before the story starts in session, and this is impossible to enforce. And I find that it is harder online, too, even with PbP because there are always some players who do not respond within reasonable time.
This is not easy, and what works in one group may not work in another, and it is rare to find a troupe with homogeneous expectations and commitment.