Determining "Edge Well" in section

[PlatteRiver]

Hello - I have the task of determining "edge wells" in each section. Essentially an edge well will be the first and last well of a section. I have the well sticks and the sections, so that part is done. What I was thinking was to add a centerpoint to each line, calculate lat/long for each point and then select the min/max point of longitude. Does this seem like a good workflow?

If so, I need help determining min/max. I'm thinking that is a custom sql statement in the select by attribute tool, but have never completed that task before. In the attached file, the 2 wells I need to select are highlighted. I would need to do this for each section, I was planning on using the iterate tool in ModelBuilder (the final tool has to be written in modelbuilder)

[KimGarbade]

A few questions.  

1)  What is a well stick (how is the data formatted)?

2)  You only want the first and last well of the section going from East to West or North to South or both (Looks like East to West)?

3) In your example the well lines (Are  these the sticks?) are mostly parallel to your East and West section lines and straight.  Is this typical, or can they be more unpredictable?  Say running East/West or turning?

4) I see in your example that it looks like two lines are almost identical along the West edge of the section.  Using the coordinates at the midpoint of the line might not give you the one you want in this case (I.E. the one that is truly closest to the section boundary.  Would that matter? Would you want to return both?