a727 no third gear

Wataminit
You HAVE to know at least which clutch does what.
You said reverse is fine
This means the L/R band is applying so the L/R servo is just fine. But to make reverse the trans also applies the Direct clutch, which works in both Low and Third gear.
This means the Direct clutch is also working.
You said second gear works, so Both the Forward clutch and the 2ND servo is working.
As to hard parts; everything is working, there's nothing to test and you didn't need to take anything apart nor install the pressure gauges.
Just by knowing how is supposed to work you have narrowed the problem down to just the Valvebody.
Now, if you install a pressure gauge you can VERIFY what you already know. And so now, you can go to the root which has to be the VB, and I suspect the #3 ball is missing, or the wrong diameter one went in there. I think it's #3,lemme check. Hyup #3

So why does it still work in reverse? Because in reverse all pressure regulation stops and the pump puts full pressure into that circuit which can be more than 250 psi........ so if you put a pressure gauge on that circuit and didn't see 250 or at least something close to it, and you knew how it worked. well, then a big red flag would go up and you'd think hmmmmmmmmmmmmmm I wonder if the #3 ball is in there.
So then you would put the pressure gauge on third gear, and run it up to third gear where you should be seeing 55 to 90 depending on where you have the KD cranked to but instead you see IDK 10 psi. Bam! up goes another Red flag, cuz you know there should be 90ish in there just before it kicks down.

So because you know how it's supposed to work and the pressures are verifying that something is wrong; your're brain combines and says
hmmmmmmmmmmmmmmmm I wonder if I put the right ball in there or even if missed that cavity.
And then you remember the ball you found on the bench, after the trans was installed.......lol.
When the trans shifts into third, and the #3 ball is not in there, then the oil goes right on by the Direct clutch and dumps into the pan, at the manual valve. That's why MaMopar put the ball in there, to prevent that from happening.
But in reverse the fluid still goes by the Direct clutch but is blocked by the 2-3 shift valve, then it backs up and pressurizes the Direct clutch, anyhow.
So I would be very surprised to see that #3 ball in there.


However
if the #3 ball is in there, the same no third gear will occur if the 2-3 valve is stuck, or if the governor pressure is too low, but your pressure gauge would not have read so low in Direct.
See that's how the pressure gauge helps you diagnose, when you know how it's supposed to work.
Finally, the 2-3 shift spring could be wrong.
So now if the pressure is right in reverse and nothing AT ALL in direct, then you go to the the governor to see if it has enough pressure to command the 2-3 shift. and if yes then you have exactly two options left which amount to the same thing; either the valve is stuck, or the spring is too stiff. Well I suppose the regulated pressure could be too low or the line pressure too low, but then you would be having other shift problems which you didn't mention.
In any case, the trans can stay up, just the VB needs to be looked at.
That's my opinion, I could be wrong