The VL-ASROC wasn't added originally because the ship doesn't carry sonar and I wasn't sure quite sure whether it would actually work without it. But, I just had the (horribly belated) realization that it would be possible for an escort to find the sub, then relay a firing solution to the Yamato through a datalink and have Yamato fire the ASROC instead, almost like an arsenal ship. I'll add it along with the RAMs that I forgot.
That works too provided you have the datalink, but even without ship-to-ship cross-targeting, you can just download target location from the ship's helos, reducing the load they have to carry on close-in patrols. VLA doesn't have range beyond self-defense against modern torpedoes anyway.
You've mentioned adding a bulb sonar, which would probably allow direct targeting of the VLA. You might want to find some space (say on the sponsons near the aft SeaRAMs) for a pair of Mk.32 self-defense torpedo tubes.
About the VLS as a whole, I did check. A 4 cell wide Mk 41 is around 125" or 3.47m. I'm trying to do this thing with 16 cell wide Mk 41s, so it's around 14m wide total. The length of the VLS was never really a concern. The Yamato's hull has a beam of 38.9m (very nearly double that of an Atago-class destroyer, which has a beam of 21m), and the forward section of the ship was also lengthened by 15m so it's not really replacing anything. Even if the forward section hadn't been lengthened, the only thing there is crew quarters which aren't too important with the reduced size of the crew. At the position the VLS is to be added, the hull is wide enough even at the waterline, which is only reached by the 64 strike length cells in the middle anyway (the 64 on the sides are self-defense length). It might be cutting it close, but there is more than enough room for the forward VLS to fit as-is, even without lengthening the forward section.
I did a quick check-fit based on the position of the VLS blocks in your drawing and a publicly available top view (of the original ship without lengthening, of course). Let's not question the advisability of cutting open a 75-year old hull to add a plug made of modern materials, that's your scenario after all.
You have apparently taken blast mitigation into account to an extent, judging by the blast shields between gun turrets and VLS, so for the purpose of this check-fit I have standardized a blast zone of 50px in front of the gun tubes.
Without any lengthening and sticking to your 16-abreast configuration, I pack only two 8-cell blocks less forward than you do, for a grand total of 288 cells. OTOH, barring other equipments, I managed to comfortable fit 24 cells abreast in three lines of 8, with space for two corridors inbetween. With that arrangement, you can pack up to 144 cells forward and 288 aft.
You might go even further by rotating the VLS blocks 90°, but I haven't tested that yet.
EDIT: Has the JMSDF ever operated (or planned to operate) the SM-2ER? If they have I might as well add that one too.
The SIPRI database mentions only SM-1MR, SM-2MR and later SM-3 BLock-3/A/B, all of which are MR missiles. That being said, I don't see what would technically prevent you from adding SM-2 Block-4 or even SM-6/ERAM since you already pack SM-3s.