Of course the clock must have run slower in the early
stages due to increased gravitational density, but never mind that.

That is why it is quite strange to set an age for the universe.

If the flow of time was slower during the first billions, than during
the last billions of years.

Then of course you will get a wastly different number for the age of
the universe, if you include the shapiro delay in your calculations.

And there is a problem: How could the Big Bang have occurred while time was standing
still?

The big bang theory is exactly what your scientists regard as pseudo-
science. Unfortunately they will not accept this for quite a while.
The ruling class always wants to hold on to the theory they used in
the past. Just like they did when they believed that your planet was
flat, and that the sun was orbiting your planet.