Look we know PLA has been playing with 1000km+ SAMs and possibly AAMs and technically ~5000km is 1000km+.
But at no point in time should we assume CJ-1000, a HCM dedicated for anti-surface roles with possible use against moving warships be assumed as the 1000km+ SAM.
First of all, if you can get ISR and stealth aircrafts close enough to reliably provide tracking and weapons guidance, then those aircraft can perform the shot anyway. You don't need a 16m long HCM for this. It's better to use that 16m long HCM against a billion dollar fully equipped warship than it is to take a shot at a AEWC or tanker. It's easier to take out that tanker or AEWC with hordes of UADF or 5th gen fighters or even forward deployed stealth assets guiding new ULRAAMs like the PL-17's replacement. Even the PL-17 off a J-16 guided by stealth ISR can do the job at 300km or greater. Even a now outdated PL-15 can do this at pretty long ranges. Yes 200km is a long range.
5000km assets aren't used to perform 1000km duties. Also would be silly to use it when 300km missiles can do the job. You can make them fast, but not that fast or cheap lol.
CJ-1000 is a revolutionary step for A2AD. Supplementing DF-26 (MaRV mach 20) and DF-27 (HGV, mach 10+) anti ship weapons. These three are all extremely long ranged, land based systems that act in conjunction with all your more forward deployed anti-ship assets like YJ-18, YJ-12, YJ-17, YJ-21, "JL-1" (it was renamed for parade to mask actual designation), YJ-15, YJ-19, and the new stealth cruise missiles. Then you have the closer ranged YJ-91 and the like. Plus a hundred other things from the past. Then you get to aircraft with lower ranged stand off weapons. At the same time you are fighting for air dominance. If you have that, the USN is going to be pushed further away.
The key is in extending this range of air dominance further from your entire ground support network. A 5000km SAM honestly has no place here despite first intuition thinking it's a good addition. No it isn't. Just add 1000km SAM to your UVLS on 055 and 052D. It'll be much cheaper and leave the CJ-1000s to harass surface combatants at 5000km.
It is technically not impossible for CJ-1000 to act as a SAM if it is manoeuverable enough. We don't know that. If it is, nothing really stopping it against heavy tankers and AEWC particularly with a massive proximity warhead. It's not ABM so it doesn't need hit to kill. In fact massive proximity warhead would be better against large aircraft.
The thing is if you have the tech to produce a scramjet powered SAM to stretch its range well beyond 1000km based on whatever your objective it and the available booster, then you can produce one that can be a ULRAAM that comes off a H-6 or H-20 or J-36. Rocket boosted AAM to mach 6 or so and scramjet powered for the rest. The calculus is target's manoeuverability. Against fighters, this doesn't even need to be considered. I'm sure MaRV, gliders and engine powered hypersonics don't have that degree of manoeuverability.