Have you tried using a "starting fluid" introduced into the intake manifold through a vacuum opening?
It should fire and run shortly if the timing and spark are right.

Have you check the plugs to see if it's getting fuel.
You had those mechanical fuel components of this system messed with. I sure hope they knew what they were doing as I doubt there are many shops or people that do.
The control pressure regulators and the fuel distributors are very precise and expensive to replace nowadays. They are very robust but you cannot, cannot, let them get dirty with old gas.

When you check that flap, by blowing compressed air under it from the air filter side, it only takes the slightest puff to make it lift when the engine is off and under rest pressure. It sounds like you have check all of that since you know it's centered.

It appears you had enough issues with the main pump. I hope you have the right one in there now.
The later LH pumps are not the same. Make sure the pumps outlet check valve is working as it may have been transferred from an old pump. It may be full of trash or have a broken spring. They used to be an $11 separate item sold by the dealer.
The replacements may fit either K or LH pumps, if you need one, but I don't know this for a fact. A check valve is a check valve though and I suspect, they didn't make two different ones to do the same job.
It's got to stop back flow or you can crank the engine for a very long time.

Also by the way there is a dot on the face of the intermediate gear that drives the distributor. It lines up to a line or dimple on the inside lip of the plastic timing cover.
It's there to locate the gear dot at the "three 'O clock" position. It's very hard to see and I use a mirror to prevent a parallax view.
One may think it's not necessary as long as the rotor points to the number one wire or lines up to that rim Mark.
This can be correct and is a reference to to use in that way. Then again, you have to remember that this is a "rubber" belt and you need to know that you have all the slack out between each of the three sprockets when you set the tensioner.
All Those marks on the belt go away on used belts so consider them as redundant not absolutely needed.
With A New or Used belt, Afterwards "always" roll the engine around, by hand, a couple turns to double check that the marks come up let alone the spark rotor. One tooth can affect performance if nothing else. A no start, no run situation calls for a broken belt check for a cam not turning.

You want the center of the rotors blade width line up to the terminal because as the engine speeds along the Sparks Duration needs to cover that width. A strobe light helps fine tune the reluctor and rotor on these years of cars up to the LH 2.4 with a CPS.

Art brings up a very valid point when he talked about that and rebuilds.
I bought a motorcycle for a $100 once because it would not start and only popped. It turned out it had a $.30 bolt broken that held the cam in place for the points. He was mad and I had the "C" note stashed away.

In closing,
It is pretty much a consensus, that we on the board, don't trust all the rebuilders. The older the cars system becomes, the more obsolete and so does the talent to rebuild them, so be aware of box stores.

Hope you find the issue.

Phil