I'd had a quick look using DUB-LHR-SIN as an example before you'd had a reply, so this may be redundant!
But you're right, BA do not offer any classes above Y on their EI codeshares.
I'd looked at BA in I class (was interested in savings, yes my mind wondered)
BA LHR-SIN in I was £3564
BA flight numbers on EI DUB-LHR and onto SIN (B/I/I/B) drops to £2115
EI flight numbers on EI DUB-LHR and onto SIN (A/J/J/Z) a snip at £10801 (note, all Business Fare Groups available on DUB-LHR-DUB)
BA metal throughout (J,I,I,J) £2118
Odd that I couldn't get the same fare using EI Prime Numbers, so well done you. My example is just a randomly picked one though!