Specifically what’s the water like north of RT4?
Hardcore
Tucker Johnson shelter has a small stream right next to it.
Rollston Rest is next to a nice brook.
David Logan shelter has a piped spring.
There are ample streams (small but clear) between David Logan shelter and Brandon Gap.
Sunrise shelter has a small stream nearby.
Sucker Brook shelter is near (guess what) Sucker Brook.
And on it goes. Each shelter has a decent water source except Theron Dean shelter, which might have water in a wet season. The Monroe skyline (from Lincoln Gap to Appalachian Gap) is notorious for being a dry area but that is due to it being up on a ridge. There IS water up there, at Battell shelter and a very reliable piped spring just before the jct. trail to Glen Ellen Lodge. From there north, get water at shelters or in brooks you come by. There is no shortage of them. If you plan your water fillups that way, you should not have any trouble.
WoodBadge
I only ever carried 1 liter during my whole 28 day end to end. no worries about water sources. just drink plenty before you leave one source and carry your liter or two and you will be fine.
Sinenomene