I don't understand how you can agree, as you did in post #30, that you can use the gravity equation to calculate that the traveler says the stay-home twin goes from 10 to 40 to 70 to 40 to 10 years old, and then also say that none of the clocks run backwards in a constant gravitational field ...

I'm not sure you've understood me correctly about the role that the gravitational time dilation equation plays in my analysis. The original gravitational time dilation equation (which I contend is incorrect, if the equivalence principle is correct) says that two stationary clocks, separated by distance "L" in the direction of a gravitational field "g" that does not vary along the direction of the field, will tic at constant rates that are different from one another. Specifically, the clock farther from the source of the field will tic faster than the other one, by the factor exp( L g ).

Now, I don't actually have any interest in gravitational fields and in general relativity. But I AM interested in special relativity, with no gravitational fields but with accelerations instead. So I use the equivalence principle (the "EP") to convert the gravitational scenario into an equivalent acceleration scenario. The equivalence principle says that all I have to do is replace the "g" in the gravitational time dilation equation with an acceleration "A", and I get an equation that tells me that if two clocks are separated by the constant distance "L", the leading clock will tic faster than the trailing clock by the factor exp( L A ).

That was a wonderful equation for me, because it would allow me to set up an array of clocks for an accelerating observer that would effectively give him a "NOW" extending throughout all space, similar to what was done so effectively by Einstein for a perpetually-inertial observer.

So I did some calculations with that equation. Specifically, I took the case where there has been no acceleration in the past, and the two clocks are synchronized. I arbitrarily choose a separation of the clocks of 7.52 ls. Then suddenly the two separated clocks simultaneously accelerate with a constant acceleration "A" for some period of time "tau" (as measured on the trailing clock). First, I do a case where the duration tau of the acceleration is 1.0 second, and the acceleration is 1.317 ls/s/s (about 40 g's). That produces a rapidity of 1.317 ls/s, which corresponds to a speed of 0.866 ls/s. I evaluate the tic factor exp(L A), and multiply it by tau to get the total change in the reading of the leading clock. The answer is 2 times 10 raised to the 4th power.

Then, I repeat that experiment, but with tau decreased by a factor of 10, and "A" increased by a factor of 10. So for the 2nd experiment, tau is o.1 second and "A" is 13.17 ls/s/s. Note that, by design, the final rapidity is 1.317 like before, and the speed is 0.866 like before. I calculate the new (tau)(exp[L A]), and the result is 1.02 times 10 raised to the 42nd power. So when we reduced tau one order of magnitude, and increased "A" by one order of magnitude, the reading on the leading clock is about 38 orders of magnitude greater than it was in the first calculation!

Then, I repeat the experiment again, but with tau = 0.01 and "A" 131.7 ls/s/s. The new (tau)(exp[L A]) is 1.27 times 10 raised to the 428 power. So when we reduced tau one order of magnitude, and increased "A" by one order of magnitude, the reading on the leading clock is almost 400 orders of magnitude greater than it was in the second calculation!

Clearly, this sequence is NOT going to converge to a finite value. The limit of the sequence, as tau goes to zero, and "A" goes to infinity (such that the rapidity and the speed at the end of the acceleration), is INFINITY. But that is inconsistent with the outcome of the twin paradox, where the home twin's age is FINITE. So the exponential equation we've been using can't be correct.

But is that exponential equation also wrong when it is used as a gravitational equation, rather than as an acceleration equation? I don't know. Maybe it works fine for a constant (in time) field that varies as the inverse square of the distance from the center of the earth. But if you do the scenario I've described for a gravitational scenario rather than an acceleration scenario, would it give the same infinite result? And would that infinite result obviously be wrong? What would the analog of the twin paradox outcome be in the gravitational case? I don't know, and I don't really care.

What I DID is develop the linearized equation that Einstein used when he was trying to figure out how to do the acceleration problem. His equation was only guaranteed to be good for very small arguments, but I noticed that for large arguments it gave results that weren't off by very much ... it almost agrees with the CMIF simultaneity. That lead me to slightly modify his linearized equation in a way that produced perfect agreement with CMIF simultaneity. But that simple modification turned out to be non-causal, and I had to make it more complicated to make it causal.

Your question was:

"I don't understand how you can agree, as you did in post #30, that you can use the gravity equation to calculate that the traveler says the stay-home twin goes from 10 to 40 to 70 to 40 to 10 years old, and then also say that none of the clocks run backwards in a constant gravitational field ..."

In the above, I don't understand why you are trying to compare a scenario in special relativity that has periods of no acceleration and then acceleration, with a scenario in general relativity that has a gravitational field that doesn't change with time. Those two scenarios aren't linked by the equivalence principle.