option 1 is better, just tell the lars youre going off freq for a minute, tell the zone you are working xxxx lars, and are making a courtesy call to advise them of your transit, especially if they have instrument procedures outside of the zone, ie holding traffic may be above 2000ft, and then tell the lars youre back on freq.
option 2 if you have two pilots, one flying using box one, your mate can use box 2 for the courtesy call.