This is personally the way I'd do a 6 day loop on the west side while getting some sleep at 5-star campsites that have (mostly) nearby water.
[ Route Editor ]
Here is some is some advice from someone who goes 2-3 times/month backpacking in the Supers. Your route is interesting and is obviously designed to cover a lot of ground - but I personally think you will be miserable trying to cover what you are trying to cover in the time available. Several sections are going to take longer than you think and are not that interesting. You will be bored to tears covering all of Boulder Canyon #103 in between Dutchman & 2nd Water. It also has a tendency to get overgrown; just kind of depends on the time of year and has frequent crossings of a usually dry creek where finding cairns and navigating large boulders can make for slow miles. The way up to Battleship mountain is a challenging day hike on its own. You will be missing out on some of the best views on Day 4 by taking all of boulder canyon - it is not very scenic until springtime when it's flowing. I would suggest Cavalry Trail instead. The views along cavalry are breathtaking. You will still get through the nicer half of boulder canyon on the way down and still have the option to turn-off to Battleship if somehow you'd have time for it. But I kind of doubt it, there are pretty long trail days. On the route I published, I have you making camp early on the 3rd day and then hiking out to Lower LaBarge box... Not to be missed.
I don't wish to deter you from your campsite plans at the big 2 springs if you're set on it. But Charlebois spring & LaBarge spring are highly competitive spots on a weekend anytime in-season, but will be difficult on a holiday weekend. T-day weekend is probably among the busiest. I would still plan to get water from those springs, but allow time for as much as a 0.5 walk from them to find a good campsite away from LOUD crowds who have already setup camp in your intended locations well before you arrive (a problem I frequently experience). Also, using the less popular campsites away from the springs, you'll have less trouble with mice... Basically what's happened in recent years is REI started to capitalize on the good weather out here in winter and offers 12 person group 'adventures' several weekends per month beginning in mid-October all the way up through the end of Spring. Those groups tend to monopolize those two springs as well as several other popular sites with good water availability. You will hear them cackling late into the night without earplugs. Just something to be aware of, that sort of thing seems to not bother some people. You can time these group activities by checking REI's website backpacking adventure calendar.
Late November tends to be a drier time of year... But you will for sure find water in the following locations which are not fire burned:
Hackberry Spring, 2nd Water spring, Lower LaBarge Box, Charlebois spring, LaBarge spring, Bluff Spring.
There is a good chance of flowing or standing pools in East Boulder Canyon along Dutchman Trail #104 - right below the section where Peralta Trail meets Dutchman.
I would not plan on finding water at Kane Spring until springtime - it's hit or miss there. I would look into Brad's Water instead. It is an un-trailed side-canyon but has cairns at the location where you exit the canyon. GPS is really important in the Superstition wilderness - Red Tanks is a trail that tends to get people lost. Here is some detailed info on getting there (it's actually quite easy honestly): Exit the trail and follow that canyon up about another 1/4 mile. Keep an eye out for cairns on the right. Exit the canyon here - it will be an obvious exit point. Travel overland east via a game trail I'd guess less than 1000 ft to a small cave which I'm 99% sure will have a large pool of water in it that you could swim in. You will pass two dry springboxes full of trashed camping gear. That's how you know you're in the right area. The route is not well marked on maps but any topo map will show Brad's Water on it. All of what I just described is easy to walk and routefind for an experienced hiker, no technical skills required. If you Search "Brad's Water" on the HAZ search, you will find some good details about accessing it. The water there is a pretty sure bet but I can't guarantee it with the fire damage and all.
The area on your Day 3: There are not a lot of reports yet about what has happened on Peter's Mesa, so you may or may not have difficulties with route finding. I would be most concerned with the condition of Red Tanks trail in upper LaBarge Box which is the section immediately north of the Dutchman/Whiskey Springs junction (what you'd be hiking a couple miles before the brad's water stuff I referred to above). You might encounter a landslide, boulders across the trail, unstable ground... or not (?). Anybody's guess really but I haven't seen reports about Red Tanks whatsoever since last spring. It was in good condition before the fire. All I know is that section of trail in upper LaBarge box was already tenuously narrow and departs along the canyon wall quite high up. I would want to be sure it was in walkable condition before doing it.
You will probably regret the campsite you planned for night 4. It's the kind of place that looks good from satellite photos (and it is a big campsite area for sure). But it's right next to one of the most popular places for day hikers to take a break and have conversations on the Black Mesa loop hike, so lots of day hiker traffic, has little to no shade, and zero water availability. I would advise hiking the extra couple miles to East Boulder Canyon on Dutchman trail. It's quieter, much less hiker traffic, better views, better shade, better water availability. At least 4 different campsites areas to choose from and decent chance of pools or flowing water.
I agree with others that SS Ridgeline is not a good trail for backpacking. Not only will it be entirely dry, there are vertical sections of difficult scrambling just below the Flatiron. Views are pretty much the smoggy dusty city on one side and wilderness on the other side.
That's a lot to digest - hope this helps with your route planning. Let me know if you'd like more information.