I did part 141 for my IR, and then flew solo under IFR (without the hood) and some time under the hood with a safety pilot (not a CFI though). The time without the hood cannot be credited towards FAA simulated instrument time, but perfectly legal for the EASA IFR time. The time under the hood can be credited towards both FAA and EASA if your safety pilot is not a CFI and he/she does not log his/her time as dual instructional time (i. e. if you are not training).
In other words, all your time with a CFI/FI usually is not PIC time according to EASA rules even it it's logged as PIC time under FAA rules. If you want EASA PIC time, you have to ACT as a PIC in FAA terms. In my case I have a separate column in my logbook called "EASA PIC" where I log my acting PIC time.
All your time under IFR flight plan is perfectly legal IFR time according to EASA rules (not for FAA though).
So if you want a shortcut, you have to obtain a FAA IR (better under part 141, it's faster and more structured), and then fly with a safety pilot under the hood and file an IFR flight plan. In that case you can log both simulated instrument time (which is useful for FAA) and IFR time (useful for EASA). Or you can just fly alone under an IFR flight plan and log IFR flight time (not simulated instrument though). After you accumulate 50 IFR hours, you're OK to apply for a CB-IR, which gives you the same privileges as usual IR (and it will be added to your license as a usual IR).
The only problem is that it's not so easy to track all your flight conditions under different regulations. But if you have (or want to get) two different licenses, you have to comply with all their rules. Fortunately I have plenty of empty columns in my paper logbook, and I also keep my electronic one.