A Bi lateral agreement could be shared authority over N reg aircraft based in Europe.
The complaint of EASA revolves around not having oversight/control over N reg so a Bi Lateral in that sense would work.
Lack of oversight is another massive misconception.
The CAA here can ground any unsafe aircraft here.
The CAA and the police can inspect any aircraft here.
The CAA here can inspect the papers of any pilot here.
The CAA can make a report to the FAA of a dodgy A&P/IA (etc) and the FAA will bust him faster than he can read this (and I know of a few who got banned from practicing for a few months, which rather tends to concentrate the mind when your livelihood is gone).
An N-reg in Europe is much more vulnerable to inspections because it has no VAT treaty protection.
An N-reg maintained here is 99% likely to be maintained by a Part M company, so it supports the industry and
helps the company to pay the CAA the annual approval fees 
The only difference is that the N-reg return to service is signed by an individual rather than by the Part M company (but under the new EASA OPS rules any "complex" will require the Part M signoff
also..... so more ££££££££ going to the local CAA
).
Does the CAA do ramp checks on G-regs? No.
Does the CAA bust EASA145 companies who use bogus-history parts and thus issue bogus EASA145 forms
and the CAA has known about them for years? No. Not, apparently, as long as the said company is paying the CAA approval fees
So, "lack of oversight" is a load of nonsense.
If I was going to operate a plane which
- has never been serviced
- is unregistered
- has a bogus number on the side
- is uninsured
- no FM Immune avionics
- runs on car petrol
and I had
- no license
- no medical
- no nuffink, never even had formal flight training but I knew how to fly and do the radio
and I wanted to fly it all over Europe, airways, the lot, what reg would I pick?
G