Three things determine the output power:
the drive level, the impedance presented by
the output matching network, and the
final transistor gain and power dissipation.
(Assuming that the supply voltage is fixed.)
Substituting a better output transistor may
help in some cases: the 2N4427 is a favorite,
while the 2N3553 or 2N3866 are more rugged
(designed for 28V aircraft radios) but somewhat
lower gain at 12V. Because they are designed
for VHF use, they will have higher gain at HF.
Other types will work as well, including those
designed for CB use.
Assuming the oscillator stage provides enough
drive, modifying the output network so it
presents a lower impedance to the final will
increase the output power.
While it has been a few years since it came out
I seem to recall that there was a following article
“Boots for the Tuna Tin 2” that was a power amp
(perhaps 5 watts output?) intended to be used
with it. That would be another approach,
especially if you are starting with an original
circuit board.
If you really want to go retro, you could use
the TT2 to drive a 6V6 or 6AQ5...