2) There is also a need to add hashes (or other identifiers) of newly discovered off-chain blocks into each block ("newly discovered" here means: not included inside any other previously reachable block). Nodes must then request such blocks if they do not already have them, and the propagation mechanisms / inv messages need to be adjusted accordingly.
Yes, this would also need to be done in order to implement your proof-of-work difficulty-adjustment algorithm, right? But it's not required for GHOST? I have not started looking into how to implement this. I am worried about the bloat that this would cause if the entire tree must be stored though. Have you looked into how your algorithm would fare if we ignored off-chain blocks for difficulty-adjustment?
This is actually required for GHOST, so that nodes have the same world-view and decide on the same leaf -- the off-chain blocks affect your choice of leaf. It is especially important for nodes that were offline for a while and want to catch up. You may in theory be able to do without it, but the convergence time to the same chain would take longer.
Regarding bloat: This is not a difficult issue. First, there is only potential bloat once propagation delays are significantly higher than block creation rates, but more importantly,
The contents of off-chain blocks can be discarded after a short while (e.g., after 1 day). Only the header is needed to verify the difficulty was met. If a switch is needed to some previously discarded subtree, then the node that triggers it, can supply the contents of the blocks as well.