Vlookup and multiple approximate criteria problem

I have been doing loads of research on this one but can't seem to find a solution. I want to do a 4 condition lookup, but for values that are an approximate match. I have seen the Index/Match formula used a lot but it seems to only work with exact matches. I've seen one potential solution using a PivotTable but I am not familiar with these or Macros. If I have to go that route then I will, but if it's possible to do this with a formula than I prefer that.
I've attached a simplified version of the huge table I'm using. I have about 24 events, a girls chart and boys chart for each event, ages 6 to 15 within each gender, 5 different results for each age, and points based on the results.
My goal: Have a formula result in the correct points for a student's event results, which may or may not be the exact number found in the table (which is why I like the vlookup because it can handle approximate values). I can alter the table if needed.
Any help would be greatly appreciated!

Thanks for the reply. I'm not sure though, how to extrapolate this formula.

I've also been working on it, trying from a different angle. This is what I came up with:

=INDEX($E$3:$E$26,MAX(IF(($A$3:$A$26=$I$2)*($B$3:$B$26=I7)*($C$3:$C$26=J7)*($D$3:$D$26<=K7),ROW($E$3:$E$26)-MIN(ROW($E$3:$E$26))+1,"")))

Maybe not super powerful, but it seems to be working for any combination of criteria I throw at it.
I'll mark it solved, but can anyone see any flaws with what I've come up with?