Quoted:
The lower nut on the "T" fitting is a compression fitting but the interior copper sleeve that it's compressing is as mentioned corroding away. Is there anyway to cut away the black plastic pipe and use the threaded lower portion of the "T" fitting?
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Not that I know of, different threads.
If you want to DIY-
You can replace the tub drain without any demo if a second person is available. You will likely need to enlarge the hole in the floor for a little more knuckle room.
1- Remove the two screw at the overflow.
2- Remove the tub flange ( top side ) with a pair of needle nose pliers or this specialty tool-
LINK. The tool is cheap.
3- Loosen the three compression fittings beneath the floor. Remove the overflow portion first. Rotate the drain tee 90 degrees and remove the remainder of the drain but save all of the parts.
4- Reassemble the old drain because that will give you the dimensions you will need to cut the new drain parts to the proper length.
5- Assembly the overflow portion of the drain to the tee. Make that slip nut tight... There is a threaded tailpiece that installs in the bottom of the tee, install that too with pipe dope on the threads. Be careful, it has very fine threads and cross threads easily. Put a new slip nut and ferrule on the tailpiece. While someone is in the tub raise the overflow pipe, tee and tailpiece beyond the ABS trap adapter and then lower it until the tail piece and overflow are in the proper position.
6- Install the horizontal portion of the drain.
You will need teflon paste and plumbers putty. Use them liberally, you can clean the excess. The plumbers putty goes between the drain flange and the top surface of the tub, never had good luck with the rubber gasket in the drain kit if it's provided for the top side. The rubber gasket for the underside is GTG. Some people use clear silicone, if you do that make sure the surface is dry and allow 24 hours before water testing.
Make sure all surfaces are clean prior to installing the new drain and it should work fine. I usually like to fill the tub and let it drain to check for leaks because of the added head pressure.
That vertical piece of ABS drain is a little too tall. It wouldn't hurt to make it shorter, just adjust the tailpiece length accordingly.