I resolved this by customizing
moodle/lib/moodlelib.php
specifically the function:
setnew_password_and_mail
more specifically, lines 5951-5953 (other lines incl. for context):
5943 $a = new stdClass();
5944 $a->firstname = fullname($user, true);
5945 $a->sitename = format_string($site->fullname);
5946 $a->username = $user->username;
5947 $a->newpassword = $newpassword;
5948 $a->link = $CFG->wwwroot .'/login/';
5949 $a->signoff = generate_email_signoff();
5950
5951 require_once($CFG->dirroot.'/user/profile/lib.php');
5952 profile_load_data($user);
5953 $a->studyid = $user->profile_field_StudyID;
5954
5955 $message = (string)new lang_string('newusernewpasswordtext', '', $a, $lang);
5956
5957 $subject = format_string($site->fullname) .': '. (string)new lang_string('newusernewpasswordsubj', '', $a, $lang);
and then I customized the "newusernewpasswordsubj" string in the language pack to use the {$a->studyid} placeholder.
H/t to Olumuyiwa Taiwo in his response to "Get Custom Fields info" and to Shane Elliott in How do I get a custom profile field in the code?Thanks eb,
Dave