I found a nice solution for this, so I will post an answer to my own question.
Basically what I ended up doing was wrapping my placeholder div inside another div with a reduced height. Then I set the wrap div to use scrollbars so I can scroll the chart.
Then I add some CSS dynamically to the tick labels to make them position:fixed and move them in to their correct place.
My placeholder div along with wrapper:
<div style="position:absolute;left:275px;top:200px;width:1250px;height:600px;overflow-y:scroll;">
<div id="placeholder" style="width:1150px;height:3410px;"></div>
</div>
My dynamic CSS additions:
$(".flot-text .flot-x1-axis").css("position","fixed");
$(".flot-text .flot-x1-axis").css("top","80px");
$(".flot-text .flot-x1-axis").css("left","300px");
$(".flot-text .flot-x1-axis .flot-tick-label").css("background-color","white");
$(".flot-text .flot-x1-axis .flot-tick-label").css("width","70px");