The issue with the part time option is what are the children who are not "in" actually doing? I assume most people would agree that an 11- 12 year old (y7/8) is not really responsible enough to be home alone from 8 to 6, and even if they were probably unlikely to come to any immediate physical harm, the probability of them doing all their set work rather than messing around on the internet is quite low. Also what is actually stopping them going off to find some mates and hang out in a park?
In some ways the motivated students in the exam years are the most capable of working effectively on line, but I'd definitely want the current Y11 and 13 (September) in as they lost a bug chunk of learning time, and the Y12s are probably less secure than in a normal year, leaving only Y10 and Y9 as candidates for part time learning - which doesn't gain much space.
With unlimited budget in the right location Y12 + 13 in written subjects (not science) could be taught in conference facilities in hotels and empty office buildings, but safe transport questions might negate the gain of rooms being larger - if schools only have standard sized classrooms I would assume that most A-Level classes would be able to distance as standard as many A-Level groups are smaller than GCSE and below.
Primary going part time would be a disaster for so many families.
The focus on keyworkers is not ideal because all too many keyworkers are a family's lower earner, and not all roles that require physical attendance at work are keyworkers (ignoring that working from home is not easy with young primary aged children that you are in charge of!)
You also have the issue that younger children are easier for parents to teach (content wise), but require more direct supervision and teaching while older children are probably more receptive but the topics covered will be beyond the expertise of many parents!
It's not an easy conundrum, made much worse by ongoing lack of investment in facilities for schools.