can do 'CFII' as initial with FAA inspector to reduce the stress/workload.
Just like initial commercial, it has to be complex (VP/RG).
Realistically, if going for aeroplane instructor, you'd most likely need CFII to be competitive. Instrument rating and commercial are requirements to do practical flight test (aka checkride in US lingo) for instructor rating, including VFR (C)FI.
Unless you have lots of twin training/time to meet the 14 CFR 61 relating to initial twin commercial, you're likely going for commercial flight test in single. If current/proficient, I recommend doing part of the CPL prep in twin, still complex, can do some instrument work in it towards CFII, if trying to cut down on the hours and 'logged preparation for flight test' as per the CFR, if you don't need much training for instrument and twin stuff.
Ground reference maneuvres have been covered above - that's where it may make sense to save on hourly rate and fly simple SEP with instructor.
If you have (I assume) twin VFR or IFR rating in Europe but not much of PIC time, Best get the 61.75 validation processed ensuring it includes the multi engine rating. This will save you the 'loggable PIC' in twin in FAA world, as manipulating controls. As in FAA system one needs 15hrs twin PIC time (ie can be further training time after/incl twin rating test), one can double-dip some of that requirment towards 'MEI' working on CFII or generally getting familiar with US airspace, maneuvres, PTS.
Verification/validation (as in 61.75) is only good for PPL privileges on FAA N-reg aircraft, but subject to flight review, can act as PIC on flight tests/rent without solo sign offs etc. That alone implies inability to use foreign crew ratings (ie FI) on N-reg aircraft in US airspace for commercial purposes. Yes, ferry flights etc may have some leeway/exceptions.