For the /3 circuit, it is improper wiring to allow currents to be unequal in any cable or conduit. That means the 3-way must be handled carefully.
As drawn, you will have two neutrals between rooms 2 and 3. They must not be paralleled, so don't tie them together in room 3! What's more, because of the equal-currents rule, the power traveling to the lamp via either traveler, must return in the neutral in that same cable.
With two groups of neutrals in the same box which must be kept separate, the next guy is likely to make a blunder. His viewpoint will be "the last guy was an idiot, why didn't he join these neutrals, because you join all neutrals right?" I see 3 ways (heh) to head off that problem.
I am a huge fan of marking wires with tape. (And cables with tape too when needed for confusion). I prefer black for always-hot, red for switched-hot, and any otherwise-unused color (typically yellow, get it, brass screws, yellow) for both travelers. (neutral must be the white wire). Because of the way travelers work, there is no need to distinguish them from each other.
So way #1 is proceed as you are and mark the wires. Mark the 3-way neutral (in the /3 and onward to the lamp) with gray tape. That doesn't come in the $4 five-packs of colored electrical tape (red blue yellow green white), so you can use green.*
Way #2 is to flip the 3-way, so the cable to "room 2" lamps comes from box 2 rather than box 3/4. In that case the wire functions in the /3 cable would be traveler, traveler, switched-hot. Those three wires would go straight to the 3-way and not splice at all, making the separation very clear.
Way #3 is to use /4 cable. Being all in one cable satisfies the "currents must be equal" rule no matter what.
* A technicality. Green is ground... white/gray is neutral... all others are hot. White/gray can be re-marked to a hot, but all other category changes are illegal, and thus, invalid. So put green tape on a white wire, it's still neutral. Doesn't work for any other color.