Best method to find variances between checkbook deposits and GL deposit transactions

One idea to consider is a recursive lambda function that processes one check at a time, assigning the check number to as many GL entries as necessary before processing the next check. 

The function RECONCILE is defined like this, with comments for clarity:

RECONCILE = LAMBDA(checks, ledger_entries,

    LET(
        // Add an empty column for the ledger check numbers if necessary
        ledger_entries,IF(COLUMNS(ledger_entries)=1,HSTACK(ledger_entries,EXPAND(0,ROWS(ledger_entries),1,0)),ledger_entries),
        // get the column with the ledger check numbers
        ledger_checks, TAKE(ledger_entries,,-1),
        // get the ledger amounts, with already-assigned amounts zeroed out
        adj_ledger_amounts, IF(ledger_checks<>0,0,TAKE(ledger_entries,,1)),
        // running sum on the adjusted ledger amounts
        scanner, SCAN(0, adj_ledger_amounts, SUM),
        // drop the processed row
        new_checks, DROP(checks,1),
        // if the scanner is zero, then the ledger check num is already assigned
        // so use it, otherwise if the value from the running sum is
        // less than or equal to the deposit of the check being processed, assign
        // the new check amount, otherwise don't change the array
        new_ledger_checks, IFS(scanner=0,ledger_checks,scanner<=INDEX(checks,1,3),INDEX(checks,1,1),TRUE,ledger_checks),
        // replace the ledger-checks column with the newly calculated array
        new_ledger_entries, HSTACK(DROP(ledger_entries,,-1),new_ledger_checks),
        IF(
            // if new_checks is an error, dropping a row has resulted in an empty array
            // which means the recursion is finished
            ISERROR(AND(new_checks)),
            // and just return the new ledger checks 
            new_ledger_checks,
            // otherwise, process the next row
            RECONCILE(new_checks,new_ledger_entries)
        )
    )

);

Assumptions:

• GL entries for check n are all added to the ledger before check n+1
• Checks table has three columns. Headers aren't important, but column 1 should hold a unique identifier for the check and column 3 should hold the check deposit amount
• The initial call to RECONCILE should have a single-column in the second argument

This assigns entire ledger entries to a single check. If the n+1th ledger entry is too large for what remains in the check's deposit amount, it won't be assigned and will be assigned to the next check. 

Applying a simple SUMIF of the GL Deposit by Check ID next to the check amount would help find rows which aren't fully accounted for. 

=SUMIF(H2#,A2:A3,G2:G9)

There are elegant solutions to finding the subset sum of a given check book deposit total.  However, the fact the checkbook date of 8/1, for example, may have GL deposits from multiple dates is the part that makes this difficult.  If we disregard the GL dates in your example, both 2500 and 4500 have several ways to arrive at those totals.   There must be something in those GL rows that would associate a given entry with the checkbook dates of 8/1 or 8/2, for example.

=IFNA(INDEX($B$2:$B$5,MATCH(SUM($F$2:F2),$C$2:$C$5,0)),"")

This returns the expected result in my sample sheet.

=SUM($B$2:B2)

This is the formula in cell C2 that creates a helper column.

The assumption is that each checkbook deposit is fully distributed to the general ledger account before the next deposit is distributed to the general ledger.