I think doing a day during the week is minimum and will give you continuity between weekends. Even 30 min easy, at night, can be useful. If you can do that a couple times then that would be awesome. Riding at night, even when sleepy, allows me to rest better and with less sleep, not sure if that would apply to you.

I used to have a pretty crazy work schedule, I think a typical one in the area where I lived. Up at about 5:30, walk to the station to catch a 6:11 train into the city, get a 7:38 train back, get back home 8:40 or so. I didn't have kids or anything so it was smooth sailing once I got home (plus the bars and restaurants were a block away). Usually I rode once during the workweek and then both days on the weekend. That was enough to keep me reasonably fit.

When I wanted to ride/race more I brought my bike into the city on Sunday, along with a pile of bike and street clothing. I'd get on the bike after work, I'd ride until something like 9, then get to the train and back home. On Thu/Fri (depending on forecast and my riding thoughts for the weekend) I'd ride until after peak train hours, get my pile of bike/street clothing, and ride the bike to the station and then home.

I couldn't take the bike on the train during peak hours, and every morning train is a peak hour train, so I had to bring the bike in on Sunday.

I enjoyed riding in the city so much that sometimes I'd take the train in on the weekend, using my train pass, ride for a few hours, then take the train back. I tried to time it so I'd be riding at night since that was most fun so I'd have to be careful not to miss the last train back (1 or 2 am).

I understand not training in the morning. I tried riding in the morning, for 5-6 months, 5:00 rides 2-3x a week, and it didn't work. 2-2.5 hour rides, I was just so slow, I couldn't work hard, and I was exhausted for the rest of the day. Ditto when I raced early (5:30 AM starts? I forget when the Prospect Park races started). We'd leave for the race at 4:15 AM. Killed me for the day.