They created a sheet for everyone that looks like this.... You can see how complex things can be schedule-wise for just one person.
The problem was that when they tried to calculate when the best time to meet would be, they got this...
...and discovered that there's never a good time to have a Team Meeting - except for Friday breakfast and over lunch on Tuesday.
I think the problem may have been our inability to imagine how to go about solving the problem, mine especially. Using lots of embedded arcane formulas in spreadsheets has always worried me. I imagine this is simple for a spreadsheet expert.
What we needed to was work out all the available times ( making them numerical rather than "IF-NEED-BE" ) and then rank those times based on percentages of all the times. This ( below ) took a few lines in Apps Script.
And we discovered that the BEST time to have a weekly meeting, based on the data collected, was Friday at 4PM.
... crazy eh?