Yes, that's also in Campbell's book: "the vertical blade, flanked on either side by five triangular teeth, was perhaps designed to cut into mud-brick". But none of this confirms it belonged to a log being carried by troops, as mentioned, it's dated from the late 5th c. BC, a time where there were already ramming "engines".   But we would need to additionally know: were they targeting stone walls? Mud-brick walls? Wooden palisades? A gate? For the last two probably it would work, for the first two, I would need to see more concrete evidence. Looking at the representation, it would seem that they are running towards the gate:

There is a theory the Olympia one was specifically designed for breaking mud bricks.  The Trajan column actually shows Dacians attacking a Roman fort by holding a metal capped wooden beam (too late for this discussion, but at least it's some evidence that this sort of weapon existed in antiquity).

I like the idea of turret points on boats. I think it would go well with #8957. In my opinion we also need some logic to allow shrinking turetable unit model's => When a unit is turreted on a boat, it become 20% smaller. Just for visual consistency with boats being a bit smaller then they should. Also as you pointed out, units should die when the boat sinks.

Maybe after being placed beside a wall, units could go slowly up, in the same way they go up when they are posted on top of walls. Would look a bit goofy right now, but still.   Yes, the Assyrians would do that to ram a thinner part of the walls. In this case, Old Smyrna 1948-1951 by J. M. Cook states that "so gigantic a mound, raised from the low ground to overtop the city fortifications, can only be explained as a siegework; and on chronological grounds therefore it can with certainty be attributed to Alyattes", which would seem to imply that they built it all the way up for troops to climb, but then it says "at a low level in the mound (about 8 metres above sea-level) a large mass of solid mud brick was encountered in our excavation; this may possibly have fallen from a breach effected in the superstructure of the city", and later on "the mud brick superstructure of the fortification there fell forward at the time of the capture or very soon after", which seems to imply ramming at a higher level. Maybe "overtop" was not literal, and the second interpretation (the Assyrian way) is indeed the faster way to do things. All this is a bit of a problem since I don't think troops carrying a log (even capped with metal) would have had enough strength to break a wall, even at a higher level. Interestingly enough, this was also the case for the Thucydides quote already mentioned, before stating the "snapped off the nose of the battering ram" bit, he says that "while raising the mound the Peloponnesians also brought up engines against the city, one of which was brought up upon the mound against the great building and shook down a good piece of it", thus, these were already engines, used in the Assyrian way. All this means that I don't see these siege ramps/mounds viable before having proper battering rams, which coincides with both appearing in Greece in the 5th c. BC, as mentioned before.   I think the earliest attestations for these in Greece come from the 5th c. BC.   In conclusion, and besides the guys with a log (after all, D. B. Campbell in Greek and Roman Siege Machinery 399 BC-AD 363 states that "it is very likely that Western warriors would soon have discovered the value of a stout tree trunk in bursting open a gate"), what seems reasonable in chronological order is: spies, climbing mud-brick walls at certain points, at some point capping the log with metal, after that (EDIT: or before, who knows exactly, both could be independent in the game) and seemingly before the 5th c. BC building a non-movable shed for it, and having ladders for the newer unclimbable stone walls.

I don't have time these days to investigate it, but the first thing I would do is follow @Stan` advice and study how it's implemented in the garrison