I'm jumping in late but are we sure that an EIP is actually a ZIP equivalent?
I have tried many times. The attached screenshot is from a hex dump showing the magic number (or magic string if yo prefer) of an EIP-file. Here is link to a list to the most common magic numbers/strings in the programming tools you use do not provide relevant info:
https://en.wikipedia.org/wiki/List_of_file_signaturesTell us about the problems you faced when you:
A) Copied an EIP file from a Capture One folder to a scratch folder outside the Capture One hierarchy
B) Renamed that EIP file changing its .eip extension to .zip
C) Tried to open the .zip in a plain old zip-tool
Actually, software that rely on the magic string/number does usually not require step B, they can handle the EIP directly after learning the magic string/number, no need for a file type extension.
As far as I know, the only embedded JPEGs are the ones created by the camera, they live inside the raw file contained in the EIP along with Capture One specific data (XML or other). The EIP/ZIP has more files and at least one folder ("Capture One").
The second screenshot is from the Windows (10) Explorer. The file 0.nef was extracted (unzipped) directly from the EIP using one of my zip/unzip tools. Byte by byte compare with the original .nef concludes "identical content". I have not investigated content of Capture One specific data files inside EIP in view of Capture One specific data files in Capture One's folder hierarchy. Did you?
Capture One preview files inside EIP, is likely negative, but you may know a trick or two here. EIPs are for moving files between instances of Capture One, and I tend to think the receiving instance may create its own preview (to fit local monitor size etc) based on the EIP content. Again. there are a few Capture One specific data files in the EIP/ZIP, it is not just a zipped raw file.