You could minimize administrative access by using a limited or custom role: https://learn.microsoft.com/en-us/autopilot/add-devices#required-permissions
If that still seems unacceptable to you, use the same script to upload the .csv output to a file share on your network.
Then you could either upload them "as is" in batches or merge them in to one bigger csv.
"The OEMs" is a very broad statement. It depends on which OEM you work with. From my time working with those OEMs at Microsoft, I can say that each one has a different approach to that. (I helped a bunch of them develop their Autopilot offerings)
I know some OEMs will provide you with whatever IDs you need at any time - even retroactively after purchase, but I also know some are super inflexible. Microsoft only mandates to have Autopilot IDs on the boxes (which are the product key IDs in that case), to be able to upload them to the customer's tenant on request and to be able to provide them to downstream CSPs.
Beyond that, many OEMs have responded to customer needs such as yours and offer both PKID and 4K hashes through a myriad of methods. Some even have self-service websites where you can submit a list of S/N as csv and you instantly get a csv of 4K hashes back.
I suggest you ask YOUR OEM specifically and explicitly how they can provide the 4K hashes to you.