The general procedure for leaning a non-instrumented engine to peak EGT is indeed to lean until there is a sudden RPM drop and then enrich to just before the drop.
This should yield an MPG improvement of 20-30% over flying full-rich, and with the normal Lyco engines is quite safe provided one does it below 75% of max rated power, and only in cruise i.e. with sufficient cooling airflow.
If this method doesn't work, there may be something wrong with the mixture linkage mechanism. Or one could have a bad spark plug or some other issue with specific cylinder(s) which gets masked by running excessively rich. For an engine to run smoothly at peak EGT, there must not be anything wrong with it.
To be fair, a PA38 is going to be old... I started my PPL in them and all I flew were not only totally clapped out but also "maintained" (by a company then holding a CAA AOC for charter) to the absolute minimum standard possible. The control linkages and the elevator trim in particular were well trashed, there was up to 1" of water on the floor after a night's rain, and the rain would fill the fuel tanks with so much water that it once took several drain beakers to drain it out, and that was just one wing tank.
A knackered 1970s C152 was a revelation after the "PA38 experience"
