How can I force HP Smart Array RAID controller to re-recognize drives?

The removed drives still have the RAID metadata on them. When you went to step #3 in the first drive replacement process; Boot up the server and acknowledge errors about failed drives, did you DELETE the removed array/logical drive or just mark it as failed? That's probably the source of the problem here.

When you brought up the system with your old drives, you should have again deleted the new data logical drive either in the BIOS raid utility or with the Smartstart/DL180 Setup Array Configuration utility and let the controller detect the array/logical drive.

Try this. Boot up with the new drives removed. Go into the BIOS or DL180 setup disk Array Config and delete the RAID 1+0 array. Then boot with your old drives and see if they're detected. Get the data you need. Remove the old drives. Delete the array. Insert your new drives. Let the controller discover the new array. Restore your data...

Keep this HP Smart Array controller users guide handy. http://h20564.www2.hpe.com/hpsc/doc/public/display?docId=c01608507

Oof, this one should have been obvious.

The E200 controller was still expecting to see the drives from the RAID10 array. When I powered up without the data drives inserted, it gave a warning about failed drives instead of an error, then let me continue into the OS. Once in the OS, I was able to access the Array Configuration Utility to "delete" the RAID10 configuration. On the next reboot, the RAID5 array reappeared as expected.

I'm not sure if this question should be deleted, since I answered it myself so quickly. But I think it could be useful for other people using HP RAID controllers.