The publically available serial number info ends with 1985.
T390XX was made after 1985, so for an exact date, you'll have to call Colt.
They'll give you a date over the phone.
However, the last serial info from 1985 was T34453, so your's is definately an OLD model gun, and will need an older barrel.
Whoever you talked to got things backward.
The OLD model barrels had TWO pins in the front sight.
The NEW models have ONE pin in the sight.
Apparently, at the same time Colt changed to the new threads, they also changed the front sight retention to a single pin versus the older double pin.
I assume, the pin change was done to save production costs, AND to serve as a quick visual indication that the gun has the new threads.
Old model Colt barrels used .5634-32 threads.
New models use.562-36 threads.
I STRONGLY recommend having your barrel change done by a REALLY Colt qualified pistolsmith.
On reason for the Python's superior accuracy is the care and techniques used when fitting barrels, and many 'smith's don't have the RIGHT tooling or knowledge.
A quick way to ruin a good Python is to allow a non-Colt qualified 'smith to do a change without having the Colt SPECIFIC tooling needed to do it "right".
If in ANY doubt, I recommend the Colt factory, or Pittsburgh Handgun Headquarters in Pittsburgh.
Both know how to do it right, AND have the tooling.
In all likelyhood, you're going to have trouble finding a NEW old thread Python barrel.
Besides Gun Parts, you can also check with Jack First Gun Parts. He's who pro's often go to first.
If you have to buy a USED barrel, BE WARY.
Often used barrels are removed because they were damaged or defective, OR they were damaged during removal by unqualified people.
Damage that can make a barrel inaccurate, or even unusable often doesn't become apparent until you try to install it.
Things to look out for:
Marks, dents, scratches, or scrapes outside indicating the use of improper tooling to remove it.
Damaged rifling.
Damaged muzzle.
Rings, bulges, pitting, or signs of corrosion.
Scratched or worn bore, or signs of improper cleaning techniques or tools that scratch or damage the bore. The bore SHOULD be mirror-bright.
Damaged threads.
Damaged or OVERSIZED forcing cone. An oversized, mis-cut cone can only be detected with a precision forcing cone plug gauge
Evidence of improper trimming of the rear of the barrel.
Cracked forcing cone.
Bent barrel (I've seen it).
Or anything else that doesn't look "right".