Thank you DalJeanis! It looks like a good solution, but the results only included the entry for "Today" and not the 5 previous weeks. I couldn't figure out what was wrong, but I'll keep looking at it. In the mean time, I've revised my solution to use a timechart command instead of stats and that cleared up my separate row issue. Now the date displays instead of "-1 Week", etc.
|makeresults count=6
| streamstats count AS serial
| addinfo
| eval thisEvent="HM1"
| eval thisEventName="Logons"
| eval subtractDays="-7d:-14d:-21d:-28d:-35d"
| makemv delim=":" subtractDays
| eval info_min_time = if((serial>1), relative_time(info_min_time, mvindex(subtractDays,serial-2)), info_min_time),
info_max_time = if((serial>1), relative_time(info_max_time, mvindex(subtractDays,serial-2)), info_max_time),
label = if((serial>1), mvindex(labels,serial-1), mvindex(labels,0))
| map search="search earliest=$info_min_time$ latest=$info_max_time$ index=ktt-prod eventCode=$thisEvent$ | timechart span=1d count(eventCode) as $thisEventName$"
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