return value of "1" if time is between (inclusive) two times PAST MIDNIGHT PROBLEM

sTUMPED! And, if someone thinks I'm attacking this completely wrong, advice welcome. I want to know the number of employees I have working in any given 1/2 hour.

in a workbook:

Sheet POSTS!:
column D is date
column E is text (employee category acronym "AA", "TA", etc...)
column G is start time
column H is end time

Sheet ANALYSIS!:
Cell B6 is 5:00 AM and each cell to the right is 1/2 hour increment to 3:00 AM, creating a GRID.
Cell A6 is date (simple enough to = referencing cell in Sheet POSTS! going down Column A).

In the grid below the timeline in Sheet ANALYSIS!, I want to return a value of "1" for every half-hour increment an employee with a particular acronym ("AA") is scheduled to work then in rows for each date above that grid total the columns for each 1/2 hour increment so I can see how many people are scheduled in any 1/2 hour.

So, FIRST: the Grid:
Some of these ending times are past midnight and, knowing Excel can't "really" tell time (midnight is 0), I'm at a loss.

example of Sheet ANALYSIS!: This employee is working 10:30 PM - 2:00 AM on the 26th.

|10:30 PM | 11:00 PM | 11:30 PM | 12:00 AM | 12:30 AM | 1:00 AM | 1:30 AM
8/26 | 1 | 1 | 1 | 1 | 1 | 1 | 1


How do I get the "1" and make sure it takes into account times past midnight?

I've tried a few nested IF's to no avail. Again, maybe this is the wrong approach entirely for counting number of bodies needed? I'm thinking Gantt, but not sure that will give me the totals by 1/2 hour.

Hmmmm. Error: File is too large (2M). Will happily email it. There's no corp sensitive stuff or anything.

How about

=--(AND(($A6+AC$6>=POSTS!$D4+POSTS!$F4),($A6+AC$6<=POSTS!$D4+POSTS!$G4+(POSTS!$G4<POSTS!$F4))))