Using SUMIF (or SUMIFS) with HLOOKUP

In cell F2:I2 i want to return the sum of columns Qtr1 thru Qtr4, respectively with the condition that Qtr1 > 0. This means that cell F2 will return the sum of column Qtr2 for the rows that Qtr1 is >0, and so on for Qtr3 and Qtr4. I want the the calculation to be dynamic in the sense that if I change cell F1 to read Qtr2, then F2 will return sum of Qtr2 >0, cell H2 will return sum of Qtr3 for all rows where Qtr2 is >0, etc.

The formula I have in place now sums up all columns correctly with the >0 condition, but I cannot change the lookup in cell F1 (e.g. change Qtr1 to Qtr2, Qtr3, etc) and also have the calculation lookup to data in columns B,C, D, etc.

=SUMIF($A$2:$A$8,">0",INDEX($A$2:$D$8,0,MATCH(F$1,$A$1:$D$1,0)))

Example Data Set:

A B C D
1 Qtr1 Qtr2 Qtr3 Qtr4
2 - 1 5 10
3 2 20 - 5
4 34 4 5 50
5 10 50 40 -
6 - - 1 5
7 6 8 9 15
8 1 - 10 50


Example of what I want to return:
F G H I
1 Qtr1 Qtr2 Qtr3 Qtr4
2 53 82 64 120

F G H
1 Qtr2 Qtr3 Qtr4
2 83 59 80



What if i wanted to add a second set of criteria? For example I only want sums of columns where both Column A and D are >0?