Hi Chris,
Adapting the K1JJ mods for the T4 to the TR3 looks possible. Here's what I would do. Admittedly, I have not moded a TR3 but I have done the T4X with great results.
http://www.amwindow.org/tech/htm/t4.htm1) Change the coupling cap at pin 7 of V14 (13DE7) from .005 to .47uf.
2) Put an RCA jack on the back panel and connect the center lug to the top of the gain pot with a .47uf cap. Shunt the RCA jack to ground with a 2-4K resistor
3) Remove the 4.7K 1W (? the schematic on BAMA is hard to read it may be a 47K) and replace it with a 5K 1W pot wired as a rheostat. (again if it is a 47K use a 50K pot)
This should allow you to adjust the carrier level and greatly reduce the controlled carrier effect. Be sure to keep the .47uf cap (C120) accross the pot.
During operation tune up to full power in the CW mode. Make sure the gain/drive pot is up all the way. Then switch to A.M. and adjust the new pot for the desired carrier.
Insert line level audio from a preamp/mixer into the RCA jack and adjust for 100% mod.
Let us know how it comes out. Ifn there are problems we can all learn. This will be good info.