I have a 64 Belvedere that has a similar problem.  I had a transmission shop many years ago look at it, they thought part of the problem is the rear servo pivot arm shaft however they were not interested in working on a pushbutton transmission.  Due to the leaks I have not driven the car other than a couple of short local trips in over 10 years.  I'm where you are, I need to get the leaks stopped.  
I like the responses you received and I'm watching for any additional comments.  I don't know beans about the 727 transmission but you may find the following link interesting.  The link also discusses a converter seal?
https://www.jalopyjournal.com/forum/threads/never-ending-727-transmission-leak.644802/
Dennis C.
On Tuesday, May 23, 2017 at 8:13:51 PM UTC-7, 62-65-mail...@xxxxxxxxxxx wrote:
Ricky asked "But seriously, how many seals are the in the aluminum case A-727?
My ’62 shifts fine, but drips – seriously thinking about taking it to Pat Blais just to replace all the seals if nothing 
else......"
So maybe we can put together a list of common failure points on the PB 727 for leaks. Here are a couple to start: 
* O-ring on the trans filler tube
* trans pan gasket
Others?
Thanks,
Gary H.