1-2 acres of watershed for a 1 acre pond in Texas sounds awfully small.
Does the pond get very low in late July and August? Does the pond get very, very low in drought years?
If not, is there some type of spring flowing into the pond?
With the 6" outlet functioning normally, does the pond have a typical "normal" water level?
The 590 tables and the subsequent calculations are very complicated because it is not an easy task to determine how much water actually hits a given pond after a big rain due to all of the variables.
I believe the numbers are usually used to get a decent estimate, and then the outlet is designed a little larger than that as a safety factor. [How has the pond done with the 6" outlet for the rains that you have observed? Was the dam almost overtopped by a 2" rain? If so, then a 4" rain will be more than 2x as much water.]
Is there any seepage around the existing 6" pipe? If not, and you are not working on dam repairs in that area, then I would leave it installed. Even if you install a new outlet, having a back-up is "free insurance" if the new main gets plugged off during a storm event.
Another factor is the amount of freeboard margin in the existing dam. If you have several feet of freeboard above the normal pool water elevation, then your pond can handle a fairly large rain event without water overtopping the dam while the 6" pipe outlet passes water.
It is not clear how deeply you are planning to cut the dam during your repair operations. Another option for you is to install a pond siphon system for your outlet. That may work well for an existing dam.
Here is a link to a drawing of a typical siphon system.Automatic Siphon Diagram
I am just throwing out some ideas. Hopefully, that will help you make some choices that fit the circumstances at your pond.
Good luck on your pond improvement project!