can't re-install high sierra and -3403F error

I went to a nearby Apple store (poor souls working all New Year's Day). A busy place. After re-explaining the problem to two more people the genus assigned hooked up the MBP to power and their network and went about re-installing high sierra. It took a while, and there was no terminal voodoo done. I asked about about and she explained it as better bandwidth. She had simply selected one of the many OS versions available on their server. Seemed a not credible answer to me, but it worked. She acknowledged that there have been 'issues' with many upgraders. I was not upgrading, but after using migration assistant was left needing to erase and re-install. Or so I thought.

As this was finishing, I asked her for a best practice for doing the migration again and she told me what they all say. I mentioned that the MacPro I was migrating from was not high sierra and she suggested installing sierra on the MBP. I didn't know that was an option, as it came formatted APFS and with high sierra. But if I was willing to wait some more it could be and we did that. She left it in a state ready to transfer data from the MacPro, which I did via a back up disk.

I have not used it a lot since, but so far so good. The unfortunate part is that I still do not know why I could not do what Apple says I can do and re-install from the internet.

Thanks for your interest.

Thanks for the reply, but I have already tried that path, several times. It runs and seems to be downloading/installing the OS for many minutes, but never completes. The cryptic error code that I mentioned is all that I am left with. I apparently should have done a backup of the new OS and contents, but did not, so that is not an option either.

Thanks for offering some detail on the error code. Your first line mentions an additional step to make the downloaded jump drive version bootable. What is that? I did that on the desktop MacPro and encountered no errors in the process.

The MBP needs to be authorized when I am in the recovery mode, but it is accepted and seems to run the download/install, until it does not complete the job. I could hook it up to the router as you suggest (have the adapter, just in case). May try that if nothing else works.

I continue to attempt to get the OS re-installed on a new MBP (15" with touch bar). Running the on-line re-install ends with a window informing me that it cannot complete because it could not create a reboot volume for APFS install. This is after I checked the OS utility and made sure the volume is formatted APFS (there are no other choices other than the encrypted and case sensitive versions).

So now I seem to be stuck with a brick. Any suggestions? I don't have another Mac running high sierra, not sure I would want that, but it is needed for this new MBP.

Thanks, again, for your several replies, Grant. I managed to get the usb drive to be seen, but was told it needed to be formatted GUID (it was HFS+). The instructions I had seen did not mention that. So I did that and went back to the MBP and it was recognized, but I could not install it on the MPB. After long runs I was told there was not enough space on the drive. I think it was trying to install on the usb drive. HFS+ is not an option in the disk utility on the MBP, which is all APFS. I even partitioned the drive, hoping to be able to install it on one of them. No such luck.

So, tired of wasting so much time, I called Apple tech support, only had to wait a minute for a well-intentioned techie to try to help. He could not, and his supervisor would not tell me what to do (it's terminal work and they apparently don't think we can follow directions). I was told to go to an Apple Store. So much for phone tech support. But he made the appointment for me (nice of him), fortunately one is not too far away and (gasp) they are open on New Year's Day! So off I go.

If you are interested in the result I will report back.