I had the exact issues you had when I converted about 4 years ago. I had plenty of hours vfr night XC in a single, but since I wanted a multi cpl, they didn't count for that box tick. An absolute joke really.
Bit late for you now, but if you did SE CPL
FIRST, then the ME CPL as add-on/extension of the single eng CPL, you'd not have to meet the usual
initial MULTI CPL reqs in 61.129.
Wonder why the school you did your flying at, didn't tell you. Probably didn't want to sell you the SE time when you could fly twin. Also, you'd have to consider the extra proficiency training for VFR maneuvres for the checkride and therefore also rental and DPE fee on top of all the other stuff in twin. I'd not do only one class CPL in fixed wing. I know it sounds silly to some, to have CPL in twin, but not legal to fly single - normally the common sense dictates that twin privileges - more complex/advanced, would mean SE built in.
For the 'standard FAA CFI' certificated, I'd need to have CPL on singles anyway, even though one can avoid having to do 'complex' portion of checkride by doing ME CPL and with 'MEI', one doesn't have to use complex single for CFI (single engine flight instructor certificate).
MHC: Well, you're right then. I'll try to look it up in the regs as part of my CASA CWLA/H self study. The US system only needs private level medical for checkrides, obviously. I'd presume it'd be similar in Australia, but had this conversion checklist, but it does indeed say 'for exercising privileges' which I didn't recall and remembered the Cl 1.
About the only shortcut is SEL/SES & MEL/MES ie do the test in an amphibian with both splashes & thumps in the test and get both classes of licence for the single test.
This could be pretty handy, if the stars align in some cases. Let's say doing MEL CPL and MEI, then SES CPL training/ride, T&G or full stop in amphib and voila! :-) Doing the ME instrument experience etc may be a bit of issue with those few classic seaplane twins in the US - would have to check. Not worth burning holes in skies at 500 USD/hr for Widgeon instead of half of that for Apache/Aztec.
Once more pressing, may look into doing the single eng CFI ride if any discount with DPE, obviously, after prior right seat flying etc. It'd not be intial CFI anyway, so don't need authorised DPE or FSDO staff examiner.