A long while back I converted an ATPL(H) to ATPL(A), although with a few more hours than yourself (4500).
I contacted the CAA and discussed it with one of their FCL guys who was very helpful. I needed to do a CPL and a multi/IR. I did the multi IR in 10 hours and the CPL in 15. Quite a 'compressed' course!
Check with the CAA as I don;t think your total is high enough to get away with the above schedule.