Thanks to Ed Himwich and Jonathan Quick, a reliable procedure for configuring the counters has been found. The key was to replace the :meas:tint? with :func 'tint 1,2'. The new counter procedure is as follows:
define counter 10278223006x "setting up agilent counters hpib=ca,*rst hpib=ca,:func 'tint 1,2' hpib=ca,:even1:hyst:rel 10 hpib=ca,:even1:lev:abs 0.9v hpib=ca,:even1:slop pos hpib=ca,:inp1:att 1 hpib=ca,:inp1:coup dc hpib=ca,:inp1:filt off hpib=ca,:inp1:imp 50 hpib=ca,:even2:hyst:rel 10 hpib=ca,:even2:lev:abs 0.9v hpib=ca,:even2:slop pos hpib=ca,:inp2:att 1 hpib=ca,:inp2:coup dc hpib=ca,:inp2:filt off hpib=ca,:inp2:imp 50 hpib=ca,:init:auto off hpib=ca,:init:cont on " hpib=cb,*rst hpib=cb,:func 'tint 1,2' hpib=cb,:even1:hyst:rel 10 hpib=cb,:even1:lev:abs 0.9v hpib=cb,:even1:slop pos hpib=cb,:inp1:att 1 hpib=cb,:inp1:coup dc hpib=cb,:inp1:filt off hpib=cb,:inp1:imp 50 hpib=cb,:even2:hyst:rel 10 hpib=cb,:even2:lev:abs 0.9v hpib=cb,:even2:slop pos hpib=cb,:inp2:att 1 hpib=cb,:inp2:coup dc hpib=cb,:inp2:filt off hpib=cb,:inp2:imp 50 hpib=cb,:init:auto off hpib=cb,:init:cont on enddef