Sounds like a perfect job for some programming. Do you have any programming experience, especially with working with files? I have tons of projects that result in output like yours, and I find it easier to write a short program than to find ways to get something like Excel to do the work. Plus even if you could get it into Excel, you'd have to manually tell it to average all those columns.
Basically do this:
1) Open the text file.
2) Read in the labels at the top.
3) Read the data in the row, storing only the data you need (row, column, index, zheight).
4) I'd have an array that looked like this: Zheight(row, column, index).
5) Open an output file.
6) Make a loop to average the Zheight for each index.
7) Save the average to the output file.
If you are an experienced programmer, this should take roughly 15 minutes to program. This is far less time that what it would take to manually force Excel to open the file and then do the averages. And if you ever have to do this again, you already have the program sitting there ready.