Hello, of course you want them to be in the same version.
One big difference will be interface numbering. This will very likely change between hardware so you'll likely have to do this part from scratch. Actually, I might even suggest you to replicate the whole vCMP host configuration from scratch since hardware differs a lot.
Once you've done this, vCMP Guest migration should be easy, I'd suggest creating empty instances on the new i7800 (since resource provisioning varies) running the same version, assign them the VLANS (naming must be the same if you want to work with UCS), perform f5mku rekeying on new guest to match the current key in old hardware, and then upload UCS file with -nolicense option.
Sorry -- I noticed you also mentioned you want to work one partition at a time.
This is a little tricker, however partition-specific configuration files are found in /config/partitions/<partition_name>/ folder.
One thing that might work will be copying and pasting <partition_name> files bigip.conf, bigip_base.conf and any additional files you might find there.
Create a partition with same name on new vCMP, move into the folder, create empty files and import text config from your backup.
The problem with this will be that you won't have all the files normally available in an UCS backup (packet captures, custom scripts, etc.) since you'll just work with text config, but it's the best way that comes to my mind to work on only one partition at a time. Also, again, be careful with network settings as there might be differences (I won't expect it on vCMPs but experience suggests "take care")
#.conf files for old vCMP was uploaded in /var/tmp/oldunit_partition1_bigip.conf
#.conf files for old vCMP was uploaded in /var/tmp/oldunit_partition1_bigipbase.conf
#step 1, create partition and confirm cfg files are present
tmsh create /auth partition <partition_name>
tmsh save sys config
tmsh save sys config
#step 2, backup current files and import partition configuration from text config
cp /config/partitions/<partition_name>/bigip_base.conf /config/partitions/<partition_name>/bigip_base.conf.backup
cp /config/partitions/<partition_name>/bigip.conf /config/partitions/<partition_name>/bigip.conf.backup
# do one file at a time
cp /var/tmp/oldunit_partition1_bigipbase.conf /config/partitions/<partition_name>/bigip_base.conf
tmsh load sys config verify
#confirm no errors , or address current ones -- it will show what line has problems in the file
tmsh load sys config # pull config from text
tmsh save sys config # push running configuration into text+startup config
#if this works try bigip.conf too
#for quick backup, copy the bigip_base.backup file into bigip_base.conf and load+save