You're both right. The ZMA SOP lists the sector name for 127.200 as "Lakeland High", even though it only extends up to FL230 (usually the ceiling of "low" altitude airspace), call it a "Low High" or a "High Low" sector. 134.55 is listed as "Lakeland Low" and sits under 127.200 extending up to 10,000 feet I believe. As noted the two sectors are frequently combined into 127.20 as required.
In any event, the feeds sound very good. Thanks much for setting them up !
JS