See Part FCL 015(d).
conversion requirements are correct, and the UK are legally and duty bound under the Aircrew Reg 1178/2011 to re- issue the CPL(A) as a Part FCL licence. It can be transferred to IAA thereafter. The medical should be accepted by CAA, but do ask them to explain their reasons if they decide not to. The usual maze of nonsense that so defines CAA and EASA!