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ThomasM125, I have the same problem as the OP regarding 1040 Schedule 1: I need to put an entry in Line 24z for the same reason as the OP (offset/zero out a 1099K Box 1a amount shown on Line 8z) but can't figure out how.

As noted by the OP, using the Step-by-Step for a 1099K, both the Gross Amount from the 1099K and the offset (as a negative amount) are placed on Line 8z.  I tried your suggestion and the result was the same...a positive and a negative amount on Line 8z. 

These approaches, which have the desired overall effect on the calculation of my taxes, do not comply with IRS guidance (IRS Fact Sheet FS-2023-06, March 2023); bold mine:

Report your proceeds (the Form 1099-K amount) on Part I – Line 8z – Other Income, using the description "Form 1099-K Personal Item Sold at a Loss."
Report your costs, up to but not more than the proceeds amount (the Form 1099-K amount), on Part II – Line 24z – Other Adjustments, using the description "Form 1099-K Personal Item Sold at a Loss.

In the example of the refrigerator sale above, if you received a Form 1099-K for $600 for the refrigerator for which you originally paid $1,000, you should report the loss transaction as follows:

Form 1040, Schedule 1, Part I – Line 8z, Other Income. List type and amount: "Form 1099-K Personal Item Sold at a Loss…. $600" to show the proceeds from the sale reported on the Form 1099-K
and,
Form 1040, Schedule 1, Part II – Line 24z, Other Adjustments. List type and amount: "Form 1099-K Personal Item Sold at a Loss…. $600" to show the amount of the purchase price that offsets the reported proceeds. Do not report the $1,000 you paid for the refrigerator because the loss on the sale of a personal item is not deductible.

Though doing so has the intended overall effect ($0 additional income on 1040 Line 10), with my 1099K being submitted to the IRS, I want the IRS matching process (if that is the correct term) to be able to find the 1099K Box 1a amount on my return (instead of net $0)...assuming the efile doesn't provide that detail.  FWIW, when I PDF my return, Line 8z shows "See Stmt"...though, admittedly, I don't know if TT e-files the two entries vice "See Stmt" and e-files the statement.  However, even if the e-file shows both entries on Line 8z, that approach is not compliant.

Thoughts or insights?

FWIW, absent a fix to this issue, as I have to file Form 8949 and Schedule D, I will create and hand-jam the losses into a Capital Asset Sales Worksheet (also from the above IRS Fact Sheet: "You can use Form 8949 and Schedule D to report the sale of a personal item at a loss instead of Schedule 1 if you wish, for example, because you have other transactions that require you to file Form 8949 and Schedule D anyway.")

Thanks in advance.

PS.  It appears that besides the above bug, TT has a bug in the 1099K Step-by-Step processing.

When I enter the amount in my 1099K Box 1a ($6738.66) and select the radio button on the subsequent page "All items were sold at a loss or had no gain" an error results on the 1099K Worksheet (aka Payment Card and Third Party Network Transactions Worksheet) on Reconciliation Line 1b (Payments for personal property sold at a loss ["Check if all" is, as expected, checked]) which shows the Box 1a amount rounded off to $6739.00...and is backlit red to indicate the problematic entry.  At the top of the Worksheet, the Box 1 amount shows the not-rounded off $6738.66.  The Federal Review explanation is "Loss from sale of personal property should not be larger than the amount reported in box 1.".  It appears that the rounded off $6739.00 in Reconciliation Line 2b is being compared to the not-rounded off $6738.66 in Box 1 versus being compared to the also rounded-off $6739.00 in Reconciliation Line 1.  The workaround to get rid of the error is to mentally round off the 1099K Box 1a amount and enter $6739.00 in the Step-by-Step form.