Projecting Project Burn Across Different Dates and Durations

I've looked at several examples but can't find something that helps me close enough with this item.
I'm brining in budgets from another sheet, same with the Start, End and Duration for each task appropriately. I'd like to project the total burn for each month associated with the project, but only for the portion of the project which would be active within that month. I've tried to incorporate helper cells to get me there, but I can figure out a way to get from A to B. My ultimate goal is to create an agile sheet that would flex as I change the schedule on another page.
Thanks so much for any insight folks can give me.
Nate
Answers
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There is a lot to work through here and to try to explain in a written answer. I would be happy to talk it through if you wanted to email me to make sure we got to the correct place with the correct formulas. Let me know!
Michelle Choate
michelle.choate@outlook.com
Always happy to walk through any project you need help with! Book time with me here: https://calendly.com/michelle-choate
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