Migration Assistant with multiple drives

We just got an iMac Pro and I've been trying to set it up from our old Mac Pro, things haven't been going great so far. They are connected to the same network. First I ran into the problem where migration assistant on the old mac can't see the new mac:

old mac can't find new mac for migration

Eventually (while on hold with support) on the new iMac I hit the back button enough times to restart the setup, and then it finally showed up on the old Mac Pro and I was able to proceed. It seems liek you need to start Migration Agent on the old mac before you start setting up the new mac.

Next problem was that once the migration was complete, on the new iMac any time I touched a file the OS would decide it was "damaged and can't be opened. You should move it to the trash." (See for instance: After High Sierra Update all files report "damaged and can't be opened")

After talking to support again and trying a few things, I'm going to wipe the drive on the new iMac Pro and reinstall the OS, upgrade the old Mac Pro to High Sierra and make a new Time Machine backup.

Next time around I'm hoping to avoid the above problems. One thing I might try different is using the Time Machine backup instead of directly connecting to the old Mac. However the old mac has two hard drives on the Time Machine backup, and I only want the contents of the system drive copied over to the new system drive. (The data drive will be connected in an enclosure.) Will Migration Assistant do that, or will it try to fit files from both drives onto the new single drive? (It won't fit if it does.)