Wow! How many solutions for a non-problem!
There is no need for an amplifier for a simple reason that the
tape output is driven by a full TTL signal. Almost 5 volts.
The reason the signal is weak at the jack is because of 2 resistors
forming a divider.
-------------R------------------->
|
R
|
___
Cut the lower one and enjoy full 5 volts. Or replace with say 4-5 K
resistor to get line level.