Help using a set of discrete cells as a range in a formula

I have a table that is generally set up like this

 

 

In each row, I have the data corresponding to a person and in the columns, it is arranged such that every 2 columns corresponds to pair of numbers.

 

What I want to be able to do is use formulas to analyze just the x-values or just the y-values in each row. But that requires using a non-contiguous range of cells and I don't know how to do that.

For example, I want to be able to add up the 10 highest values of y for each person (row).  Normally, i would use "=SUM(  LARGE(  B3:G3,  {1,2,3,4,5,6,7,8,9,10}  )  )". But I can't do that in this situation because I don't know how to format a non-contiguous range of cells in such a way that it can be used as an array variable in a formula. How can I just use "C3,E3,G3" as an array?

 

I've seen that it is possible to do so with named ranges. I can do it that way such that the formula looks like "=SUM(  LARGE(  Range_1,  {1,2,3,4,5,6,7,8,9,10}  )  )", but that's not really a scalable solution for me. I have almost a thousand rows and I'm definitely not manually creating a named range for every row. Especially because I frequently sort and reorder the data in various ways.

 

SSo How can i use a range of noncontiguous cells as an array parameter in a formula?