Here's a rough shot at what would seem doable to me as far as a Chinese program, with "enough" budget, but nothing "crash program/super urgency":
1972: IOTL, Shuguang capsule program cancelled and astronaut group dissolved after they realized they needed a final budget infusion to meet the 1973 goal and reach first launched. ITTL, whatever the politics, they get one, as well as approval for a limited station program
basically stealing this. Development approved on various small N-Room Stations and a Suguang with rear-mounted docking ring, hatch, and control station.
1973: Early test flights of FSW recoverable satellite (recon) and late in the year, first unmanned flight of Suguang. In triumph, CZ-2E equivalent approved (*CZ-2E from here on)
1974: Early Shuguang flights, perhaps two or three? Starts with relatively short flights, then moves to longer durations (couple days? EVA?)
1975: More Shuguang flights--Continue EVA? Rendezvous w/o docking between two capsules, or capsule and an unmanned FSW?
1976: Introduction of "dockable" Shuguang, first Chinese docking in space (Shuguang to One-Room Station, launched on seperate CZ-2C launchers). Roughly 30-day durations. Second One-Room mission, 60 days. First test flight of CZ-2E equivalent, ~9 tons to LEO.
1977-1979: Two-Room Station introduced. Since it's resuppliable, it makes use of this to launch heavily stripped-down on a CZ-2C, requiring extensive fit-out on orbit. Anyway, it's got a couple spare mooring ports where spacecraft can be moved once they dock, and we see the introduction of a 3.8 ton Supply Module. Capable of supporting four astronauts for brief periods, or two for much more extended ones, it's certainly matching the superpowers: Shuttle Spacelab missions are similar duration and capability, but lack the "drama" of a space station that stays up (despite there being at least some arguable utility in getting the whole lab back, and it has many more crew available to work in the lab while it's up), while Salyuts at this point are 3-man affairs, occasionaly jumping to 6 for handover. I'd expect to start seeing reaction to China appearing in the Us and Soviet programs about now. For the Soviets...more money for Buran and Mir? Maybe they focus on TKS as a crew vehicle, seeing the benefits of capsules? For the US, maybe an earlier alternate Freedom-like program, begun under Carter, or something like the
Science and Applications Manned Platform which was basically a large power truss, which then was expanded into a man-tended lab then a full station by repeated additions of shuttle-launched modules on every support flight? Anyway, kicks in the butt all around.
1980: First CZ-2E launched station, the "four-room" consisting of 2xTwo-room, one optimized for living and lab space, one for power production and systems support, bolted together on the ground. Capable of supporting six for brief periods, but probably more like a 4-person crew. That'd be two crew of 2 on station, staggering rotation of one crew every 30 days or something (for ~60 day total stays) or 45 days (for ~90-day total stays).
The early 80s are then consumed for the Chinese with operating and expanding the four-room station, operating Shuguang/Supply Ship combos to it. Maybe a one-off One-Room+depeleted stage artificial gravity demo flight? That'd be a heck of a way to stick one to the US and Russia while still doing really useful science. Anyway, I'd say around 1983 you could start seeing moon missions as a potential for approval, but if the approved plan is anything more than flags-and-footprints, I can't see any hardware actually beginning operational flights before the 90s, not with the stations to operate. Assuming a ~1983 lunar mission program approval, based on using a manned fuel station as a base for refueling modified upper stages:
1983: Approval granted for EOR-based fuel depot lunar mission program. New fuel depot will be based on Four Room station, with additioal equipment to support cross feeding of fueling lines from the various docked supply craft to a docked modified upper stage. New hardware needed: lunar return/extended-duration Shuguang, a couple different upper stages (a Small Stage of ~7.7 tons gross mass and a Big Refuelable Stage of ~4.7 tons dry mass capable of holding about 52 tons of fuel), and the all-important
lander (roughly 10.5 tons gross mass, a really stripped-down 2-man vehicle).
Mission Plan: Big Refuelable Stage burns to place the stack into a free-return trajectory. After a year to fill the blasted thing, it goes sailing off into interplanetary space, or you can get cute and aim it at the moon to create seismic events for the detectors left behind by Apollo--two points for hitting the Eagle, one point for taking out any other hardware. The Small Stage is used twice, first to place the stack in lunar orbit, then to get the capsule back home at the end. The lander does what it claims to do.
1986: First of the 7.7-ton upper stages flies aboard a CZ-2E, and docks on automatic pilot with a pre-placed "circumlunar FSW", modified for lunar return capability. The stage is then tested by burning this stack out of LEO and into a loop around the moon. Upon the recovery of the FSW and it's precious onboard film, China has its first high-quality imagery of the lunar surface. Repeat as needed to get good imagery of all landing sites--this may take several flights, but that's okay.
1987: Ongoing FSW circumlunar flights. Note at some point, you can easily swap out the FSW for a Shuguang, and get the prestige of being the second nation to put men into lunar space (though not orbit--yet). New "fuel depot" flies, and the first Big Refuelable Stage flies to dock with it (carrying about 4 tons of fuel inside it to start). A series of tankers (derived from the Small Stage with precision manuevering engines and docking systems) arrive at the station, each transferring 7 metric tons of fuel into the Big Refuelable Stage. It takes about seven flights to fill the big stage all the way, less for a partial fill.
1988: Apollo 8 redux. Take a partially-fueled Big Refuelable Stage, Shuguang, and a Small Stage. Big Stage to TLI, Small Stage to get Shuguang into and back out of lunar orbit.
1989: Test lunar lander in LEO (slightly short-fueled, launched on CZ-2E). First unmanned operations, then later in the year first docking of the lnader and the Shuguang to test manned operations.
1990: Well, let's go to the moon: take the first fueled Big Refuelable Stage, a Shuguang, a lander, and a Small Stage. First flight I'd recomend either as an Apollo 10-style near-landing with fire-in-the-hole abort test, or an unmanned landing with the crew staying in orbit.
1991: After laboriously filling another Big Refuelable Stage, go to the moon again. This time, stick the landing. Or don't. Either way, give a speech about the surviving Spirit of Communism because the Russians need more to cry into their vodka about in this moment of national loss as the country comes down around their ears. There's been 13 years of butterflies in the US program by now and 8 years of you specifically saying you're aiming for the moon, so be prepared to be friendly with any sort of US, or joint US/ESA lunar landing crews you may be sharing the moon with. Try not to look too longingly at their hydrogen engines or video of their 20+ ton launchers, you got here without them, right?