As far as I know, and I am myself undergoing the FAA IR now, if you get the FAA Multi IR it works for single engines as well.
On the other hand, some of my friends doing single engine FAA IR including conversion to CAA IR (15 hours) said, they also would had to do additional hours to get JAR multi-IR afterwards .
In regards to doing JAR or FAA IR, it is by far cheaper doing it FAA. The talk has bin going on, that their actually might be a chance a convertion of FAA to JAR IR without additional training is possible in the near future.
Aside from that, a Ceneca is about 900-1200 eu hourly last I checked and its down to 250$ in Florida where I am now.