Calculating scheduled hours per resource between 2 sets of overlapping date ranges

I need to calculate a sum of hours scheduled for each resource for each week from a work schedule that lists the resource, start date, end date, and hours per work day. I can do this with the use of helper tables/columns, but I need to be able to perform this calculation without helpers.

I have attached a "sample" which contains all the details. I need the desired table with ?'s to have the same answers as the current table only without the use of the helpers (or significantly less helpers).

Thanks for your help!

Clear all expected results.
Try this in W14.

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Thanks windknife! This worked perfectly. I appreciate your help!

You are welcome.