convert SUMIF to SUMPRODUCT Formula

Its my first post here so hopefully you'll go easy one me

Im trying to find a solution for my report.

I have a basic SUMIF formula returning correct results, but the report I am working with is reporting monthly data. When I insert a column for the latest months data, with the SUMIF formula, all the relative references move along so that the current month column is excluded from all the formulas. I tried using $ in the formula but that didnt seem to fix it.

To solve this I added in a SUMPRODUCT with VLOOKUP, hoping that with the VLOOKUP added, the index numbers would remain accurate even when a new column was added.

However my SUMPRODUCT with VLOOKUP isnt working properly, when the lookup item appears twice or more in the data set, the formula only seems to be picking up the first entry and not summing all.

There must be something really basic wrong with my formula. Hoping its an easy fix

=(SUMPRODUCT(VLOOKUP(C5,'DETAIL DATA'!H:AH,{2,3,4},0)

Or even just this to just get a single column (same result as SUMIF formula), will it work, or what is the fix?
=(SUMPRODUCT(VLOOKUP(C5,'DETAIL DATA'!H:AH,{2},0)

Ive attached an extract from my report, can go to SALES BY CUSTOMER sheet and cell E5

Thankyou Ford! That works perfectly for the single month that I use your date formula for. What if I wanted to have to formula add up a few months eg, July, August and September, and put result in a single column (eg column E of my Sales By Customer sheet). This is what I was trying to do with the formula I posted above

=(SUMPRODUCT(VLOOKUP(C5,'DETAIL DATA'!H:AH,{2,3,4},0)

I appreciate your help thankyou!