Is there a shift kit I can install without removing transmission to give me a longer shift from 1-2 and a firmer shift from 2-3?

You can get later and slightly firmer shifts simply by lengthening the TP linkage.

Depends on the type of linkage, with the three-piece linkage you can just unthread the slotted end on the top rod; unthreading the end makes the linkage longer.

is this internal or external?

External. Check the various linkage configurations in the archives link below, the slotted rod is visible where the lingage attaches to the carburetor throttle lever.

http://www.moparts.org/Tech/Archive/auto/35.html

Don't get carried away with this though as going too long will limit your wide open throttle by not allowing carb to open fully.

Whan I adjust mine, I hold the throttle wide open then adjust the linkage so it pushes the transmission arm all of the way back for full open.
Then if the shift is to late you can adjust it back two turns or 1/8" at a time.
But I have always used the TransGo TF-2 kits for 40 years and always set the transmission arm adjustment at full open and the shifs are great.
A little hint is to remove the throttle return spring when making this adjustment so you do not flood the engine during this process, but be sure that you put it back in when you are finished with the adjustments.
Your second question about the stock shift being bad is because the design of the 727. The 2-3 shift is done by the second gear band still on when the 3rd clutch is applied causing a overlap or bind up. What the transGo kit will do is change the timing on this by applying more preasure on the 3rd clutch pack and change the apply timing with a restrictor.
If you look at a chart lets say a stock 2-3 shift is 2" wide the TransGo shift will be 1/4" wide.
In fact my Cuda would bark the tires going into 2nd and squeek them going into 3rd.
But when driving aroung town or crusing the shifts are mild so you are not jerking everything loose.