You will need a area of your spreadsheet set up for intermediate calculations. You could use any place on this sheet, or even another sheet. I think you could then write a macro that would sort each line individually in the intermediate area and leave the original data unsorted; however the following method should give you the results you want without a macro.
For this example, I am inserting 11 columns between Loc8 and Total (J through T).
After the formulas are all entered, you can then hide these columns. You could also put these columns elsewhere as mentioned above, and adjust the formulas accordingly.
J: =MINA(B2:I2) *** find first minimum value
K: =COUNTIF(B2:I2,J2) *** count occurrences of this minimum value
L: =IF(B2=$J2,300,B2) *** get Loc1 value unless it is the min. value, in which case make it a large value (i.e. 300)
M through S: *** copy column L into these columns.
T: =MINA(L2:S2) *** find minimum value of new table.
U (Total column): =SUM(B2:I2)-(IF(K2>=2,J2*2,J2+T2)) *** This takes the sum from the original row, subracts from it either: (first min. * 2) if 2 or more occurrences, or if only 1 occurrence, subtracts (first min + 2nd min).
This will give the total of the top 6 values for this row. You can then copy J through
U down as far as you need to cover all runners.