Under the FAA rules, if you are appropratly rated for that Aircraft, you can log time as P1s, if you are under further instruction.
Go to the Orlando "FISDO" get your CAA licence converted to a FAA on the spot and free, YES CAA people INSTANTLY and FREE!!!
Then you can get instrument training and log it as P1s, This can only be done simulated IF, as long as you maintain the requirements for VMC, you are still able to act as PIC. Be aware for issue you need 50 X-Country, this is a distance greater than 50nm straight line between depature and destination. (not the extended downwinds in britain) but this can be done during IR training.
The instrument time is great experience, even if you don't get the IR,
A Multi is a must in the states, its soare so much cheaper it's worth it just practice for over hear, but its only Pu/t
Bashing holes in the sky really isn't to constructive, an instructor constantly pushing and giving advice is worth the extra money IMHO