Yep, I think that's the right log. I see it's not just modded TEs, but also vanilla TEs which are failing to load.
My first guess is world corruption, which you already tested for ofc, but there is always the possibility that you were not loading the corrupted *part* of the world in the SP test? Generally, world corruption is not the entire world, but rather certain chunks, so if those chunks were being loaded in multiplayer mode but not SP mode for some reason...
Other than that, I didn't come up with any good ideas from the log (unless you count "maybe the SF4 team will have a better idea when they see this log").
Just for reference, how much RAM is the server allocated? I think when a player dies and respawns, the chunks at their respawn point load before the chunks where they died are released (though I'm not sure, so don't quote me on that). If this is true, and the server was already near max memory capacity, I could see it possibly causing corruption.
In any case, I'd suggest going to their issue tracker that I linked to in my previous message, and posting a new issue for this, with a link to this thread for reference. Even if it does end up being world corruption and you manage to wipe the offending chunks, it would mean that something somehow caused said world corruption, and it might happen again. And I could also be way off track, so getting them to take a look is probably a good idea.
I don't see anything about "skipping block entity" in either of those, so I'm guessing they're not the logs I'm looking for. Generally, the logs you want are the ones found in the "logs" folder of the server and the client with issues. If you just ran a session and had an issue, it will be the log file named "latest". Otherwise it will be one of the others (or if the problem was too many runs ago, it will be gone).
I took a look through the MC code a bit, and that error is (as you might expect) just a generic "Hey, something went wrong" error. The things it can trigger off of are not specific enough to give me any solid clues. (If anyone is interested, it's in TileEntity.create() )
(TileEntity == BlockEntity; somewhere along the line, the most common name switched from BlockEntity to TileEntity, but they're the same thing)
You could also try the skyfactory 4 issue tracker, but I can almost guarantee they will also want that log file with the error message you mentioned in it.
Even just the mod listings in the log file are useful, and fairly often there is a little message somewhere that is overlooked (though I'm not saying that's necessarily the case for you here). I'd pastebin/hastebin and link it here just in case. I haven't played SF4 yet, but I'll at least look at the log file and see if I notice anything new, if you post it. I can also scrape through forge's code since I'm a mod dev myself and see where that particular error is triggering from in code (assuming the message lives in MC/Forge, and not in one of the mods in the pack).