Ralph,
It's hard to tell what's going on, but here are a few thoughts.
The two captures that failed failed in exactly the same way: The checksum of the record at file offset 992,333,119,488 was inconsistent with the data. The position was the same and the (bad) data was the same both times. This would indicate a permanent media failure. The data stored on that portion of the drive is incorrect, and remains incorrect, after being repeatedly re-read.
Another type of error is a transient error, where the data is stored on the media correctly but gets randomly scrambled on its way to QRecall. This kind of error isn't repeatable.
When you ran the repair, you got a massive number of data corruption errors. Since you ran disk diagnostics on the volume, we can assume these are not the result of cross-linked files.
I conclude that either the drive is experiencing rampant media failures, or the archive data was scrambled while it was being duplicated. (This latter theory could be explained by transient errors, but you'd have to get a lot of them.) I would bet on the former, since you successfully captured data to the new archive immediately after the copy. It seems highly unlikely that the copy wouldn't result in any damaged records that belonged to the first computer, but munged thousands of records belonging to the second.
Regular disk diagnostics (i.e. Disk Utility) will only tell you if the volume directory structure is correct. There are extremely few utilities that will perform a surface test. A surface test writes a pattern of data to every sector on the drive, and then reads it back to make sure it's still correct. These tests can take hours, if not days, to complete.
It's immaterial whether the data on your drive is encrypted or not. It only matters that it's written and read correctly. I don't need to know anything about the data to write it and look for any discrepancies when it's read back.
Having said that, you can easily perform a surface test yourself, since your archive is so large and would cover a significant portion of the volume. Erase the new drive and start over. Copy archive #2 to it again. After writing it, verify the archive or use the command-line
cmp tool to perform a byte-by-byte comparison of the original and the copy. (Make sure you've placed your QRecall actions on hold so the original doesn't get modified during the copy.)
If this is successful, move on to trying to use the new archive again and note at what point (using it on the laptop, for example) the problems reappear.
If the comparison test fails, you've narrowed down the problem to either the drive or the busses (USB) you're using to transfer the data. Which is to say, you haven't really narrowed it down at all.
The next step is to use a different interface. If the drive supports both FireWire and USB, switch to FireWire, or eSATA, or whatever you've got. It's a little geeky, but I keep a spare external drive enclosure around just for testing drives in an enclosure with an interface I trust.
If, after performing the copy and compare again using a different interface, you get the same kind of data corruption, my money would be on a bad drive. If switching interfaces cures the problem, then that's where you need to look next. It could be a motherboard issue with the computer or (more likely) the interface controller in the drive's enclosure.