You are referring to a pro-rata calculation.

HAM-DXB-CPT-DXB-HAM is 25,017 km.
DXB-HAM is 4,888 km. That is 19.5%.

OP got 8% back.
8% in 19.5% is 41%.

How do you actually calculate this "actual cost difference"? This is the big question.

If this goes to trial, EK has to lower its pants and detail out how it got to these 18%. (corrected: it is 8%).
I dont think Emirates is keen on doing this and is rather willing to settle in this case.

I wouldn't be so sure - Emirates does not seem to shy away from litigation.

It was party to the Schenkel decision about the applicability of 261/2004 in the ECJ and is also the party to the test case in the Court of Appeal in England about whether 261/2004 applies to mis-connections in DXB causing a delay at the final destination in Emirates v Gahan.

I think there was also a thread on here a year or two ago where EK's final decision in writing was that they used a pro-rata great circle distance then compared that to the total fare in the lower cabin calculated on the day of the change and gave the difference pro-rated.

I don't think that would hold up in court.
The fare difference on the day of booking between the actually booked F fare and the corresponding C fare with similar restrictions should be applicable.

Your math almost holds up. As I already stated and you concur it is 19.5% of the total ticketed distance that is affected by downgrade. OP indicates to have been offered 8% of total ticket cost as refund. If F was indeed roughly double the cost of J on the day of purchase that is an accurate calculation and compensation should indeed be in the 7-10% range.

I agree - your analysis seems more equitable than EK's in that previous case.

That said, if he was travelling on an F/A class ticket but only sitting in the J cabin, EK could potentially argue for the access to additional baggage allowance and F lounge access in DXB.

Now, that would be an interesting cost claim!

Wouldnt the passenger be entitled to F lounge access, because he arrived in F from CPT - even if the traveller continues with EK in Y or C?

No

EK allow lounge access based on departing flight - usually in the case of a 2-class downgrade, they will look at the fare basis: if the pax is still booked in the onward F/A/Z fare buckets, they will have F lounge access in DXB. If they've been rebooked into the C class buckets, then only business lounge access.

Let's see if the OP ever returns to update...