"I'm asking whether it is okay to group the whole thing together as a collection of averages" Yes and no. You can group the sale together and report the entire selling price. Your cost would not be an average since you do not have the actual numbers, you would not be able make up a number based on your assumptions. You would need to add up each item individually. If you do not know the number and you are sure all items cost at least $1 each, then you could use $1 for the ones you don't know.
Your selling price is not in question at this point. You just need to determine your cost basis.
In other words, when trying to give a fair estimate of the original cost basis, is it okay to average it out for everything? No. For your basis, it is best to find some type of documentation or look up selling prices around the time the items were purchased. You cannot just assume they all cost the same. If you were audited, then you would need some form of documentation (even if it is research) to substantiate your claim for the basis. If you have absolutely no way of knowing and you cannot provide anything to say that your estimate is reasonable, if you were audited, the IRS could decide that your basis is $0. If some items cost $1 and some cost $40, but you have no way of knowing which ones were which and how many of them were at which price, the best answer is the most conservative answer. The selling price in no way shape or form affects your cost basis. So, you can't just average it out based on the increases and decreases. The IRS will look at these numbers separately.
When you do come up with it, a spreadsheet of the sales price and costs, would be a good thing to keep with your tax records for 2022.
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