FYI, I used the format visualization option which populated the proper code into the panel, then since the format menu only allowed ranges, I used your code to modify it to a single value. Here's the result:
<row>
<panel>
<single>
<title># of Systems</title>
<search>
<query>sourcetype=prod source=*peek.log config_section_stats | stats latest(_time) as latest_log_time, latest(model_time) as latest_model_time by case, source, hostname | convert ctime(latest_log_time) | stats dc(case) as NUM_LINES</query>
<earliest>-15m</earliest>
<latest>now</latest>
</search>
<option name="rangeColors">["0xffffff","0xdc4e41"]</option>
<option name="rangeValues">[44]</option>
<option name="useColors">1</option>
</single>
</panel>
</row>
... View more