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