Update spreadsheet values based on separate data, by changing the date in a single cell.

I inherited a nightmare pile of spreadsheets in my new job. I work for an energy engineer on a military installation and track the energy usage and costs. My predecessor had a couple of dozen, loosely organized spreadsheets he updated each month with a lot of redundant information.
The most time consuming is one with all the reimbursable accounts. In the old system, it took two full work days to update all the information, but as I've consilidated the spreadsheets and manage the data better, I'm down to half a day. My goal is to update one cell or the current month, and have all the relevant cells update. So, from two work days, to two minutes.
The big challenge with this spreadsheet for reimbursables, is that it is generated externally from my organization. So, even though it's poorly designed and clunky, it's the same spreadsheet they've used since 2002 and they aren't going to change it.
The way I have my data set up is that each energy usage type is on a separate spreadsheet within the workbook. Each month I get readings from the shops who go and read the meters. I have a tab for water, natural gas, and electricity.
What I would like to do, is to go through each cell where I have to update the reimbursable amount, link it to the meter reading for that month, and have it update based on the new month selection at the top of the worksheet.
For example, if I change the spreadsheet from September to October 2020, I would like the cell for electricity for 1234 Delaware Ave to gather data from the electricity tab, but move from the September column to October and so on. But there are 50 buildings or so on the spreadsheet, and each has reimbursibles for water, natural gas, and electricity.

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Perhaps the following would help.
Rename the McGuire sheet tab so that it reads Sep
Paste the following formula into cell C146 on the ANG Worksheet sheet:

Formula:

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Paste the following formula into cell E146:

Formula:

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Let us know if you have any questions.