The problem would be the same as far the ratio is concerned. One has a .67 and the other .70 overdrive. I didn't know they made a long shaft 350, so the one you have is a normal shaft.
An overdrive will do you little good and a 350 Turbo replacing a ST300 is a good swap. Your drop in first gear ratio will make it seem like to put 4.10s in the rear from a start but still have 1:1 top gear for cruising. Don't let the passing gear detent cable mess you up. Even without the automatic drop down will still have better performance.
Depending on the travel of the kickdown lever on the transmission, it would seem that possibly a throttle kicker solenoid might be able to be used to provide kickdown. That way, the OP could keep using the kickdown switch on the carburetor for kickdown.