If you can't fly today on your EASA licence then you can't fly today on your Part 61.75 FAA certificate. Unless I'm wrong, in which case I'll be happy to be corrected.
John Lynch of the FAA used to provide a Part-61 FAQ. It bore the following notes:
Disclaimer Statement: The answers provided to the questions in this website are not legal interpretations. Only the FAA's Office of Chief Counsel and Regional Chief Counsel provide legal interpretations. The FAA's Office of Chief Counsel does not review this website nor does it disseminate legal interpretations through it. However, there are some answers provided in this website where the FAA Office of Chief Counsel's legal interpretations have been reprinted.
The answers in this website address Frequently Asked Questions on 14 CFR Part 61 and represents FAA Flight Standards Service policy as it relates to this regulation. The answers are in response to questions from FAA Flight Standards Service’s Regional Offices, District Offices, and concerned people from the public. The answers reflect FAA Flight Standards Service’s policy for the purpose of standardization.
While the document has now been withdrawn, I have no reason to believe the policy has changed. It addresses the issue at hand directly:
[The first part of the question was about whether a current rating is required for an initial 61.75 issue – the answer was no.]
QUESTION: Secondly, it is my understanding that once a § 61.75 U.S. pilot certificate is issued, it confers piloting privileges (provided the pilot holds the required Part 67 medical certificate and is § 61.56 flight review current, § 61.57 current, and is § 61.58 PIC current if § 61.58 applies for the kind of aircraft being flown), irrespective of the absence of current foreign proficiency checks on the foreign pilot license. Under U.S. rules the person’s foreign pilot license must remain effective [pursuant to § 61.19(c)], but again the word effective means the license has not been “surrendered, suspended, revoked, or expired” [See § 61.19(f)]. In other words, under the U.S. rule, the lapsing of a pilot's foreign proficiency check does not mean the person’s foreign pilot license has been “surrendered, suspended, revoked, or expired.” A foreign pilot license remains “effective” even if the pilot may not exercise the privileges of that license (because the pilot had not completed a U.K. proficiency check). Is my understanding, that under these circumstances the foreign pilot may still exercise the privileges of his § 61.75 U.S. Private Pilot Certificate, accurate?
ANSWER: Ref. § 61.75(e)(3), A person may still exercise the privileges of his U.S. § 61.75 pilot certificate provided the person has met U.S. Part 61 currency and recency of experience requirements. The exercising of a person’s U.S. § 61.75 pilot certificate is not contingent on whether a person has completed his U.K. proficiency check. Only when a person’s foreign pilot license has been “surrendered, suspended, revoked, or expired” does it effect the privileges of the person’s U.S. § 61.75 pilot certificate.
{Q&A-656}
QUESTION: Finally, it is my understanding that the fact that the foreign pilot license bears a lapsed proficiency check does not mean the FAA considers the foreign pilot license has been is limited or restricted under § 61.75(e)(3)? It is my understanding that the phrase “limitations and restrictions” under § 61.75(e)(3) refers only to pilot-specific restrictions such as prohibitions from night flying. Is this correct?
ANSWER: Ref. § 61.75(e)(3), Even if a person’s foreign pilot license bears a lapsed proficiency check it would not effect the operating privileges of that person’s U.S. § 61.75 pilot certificate.