This is why I put off doing techie things... it never goes to plan.
So, end of long story, Titanium Backup is not able to restore missing apps+data. It says that there are no backups made. Instructions say to manually put the backups folder onto the SD card. I have done this (twice - once to external and once to internal SDs because nobody specified!) but Titanium still can't "see" the files. I tried the simple Dropbox syncing and all it did was delete what was in Dropbox (I have copies elsewhere!).
So, uh, yeah. Now what??
I can manually reinstall new apps but that doesn't solve the whole Titanium-backup-is-basically-pointless-if-it-doesn't-restore aspect.