throwing in my 2 cents from europe
Laws apply to the roads you are driving on and this means each vehicle using this road needs to comply. point. You might get away with it if you meet a friendly uniform but they can also see you as a money-source. (in many countries their payment bonuses are directly related to the penalties they write out in that given period)
I illustrate with a different example, since January each car needs to carry a breathalyzer (alcohol tester) in france. No matter from where you come or what you are driving you need to have this on board or can be fined. Some countries you have to have a fire extinguisher; some not, some it has to be mounted in-reach of the driver, others it does not matter, some countries you need a reflective vest for each of the passengers and driver, some only for the driver etc etc
Your trailer needs to comply with the laws valid for the road it drives on. NO MATTER where it is registered, or which license plates it has. (exceptions are diplomatic vehicles or army forces deployed in foreign territory)
trailers with max gross weight less than 750kg = license plate as the car has IF your car insurance covers the trailer also (which most insurances do here).
It will need to have a technical type approval, made by a constructor and technical control; this is EU-wide valid and it might be possible to obtain this based on your US type approval. (took me 2 months to register a UK made trailer in slovakia as it was first time imported into that country)
Trailers with max gross weight over 750kg = separate license plate, yearly technical control and separate insurance and the trailer must have a active brake system.
With your 110 you will need a driver license equivalent to the european B+E type. (max gross train weight over 3.5 ton and below 7.5 ton)
(if your vehicle or trailer are registered to a company you open up a complete different can of worms which includes tachograph, drive-time limitations etc so hope you have it all on your personal name and dont fall under commercial transport)
Speed limit for trailers is 80km/h in most countries. IF your trailer is type approved for this and your car has ABS limit is 100km/h.
Tow hitch needs to be type approved on all non-commercial cars. The system you mention is not. i also have no knowledge of type approved 4" hitch systems in europe.
So this is another registration you have to go through.
Regarding insurance make sure your insurance is valid in europe, and in each country you are driving through. It is not because your insurance says it will cover you that the insurance company is recognized over here. Ask them which european partners they have or under which insurance license they are registered. Might save you a lot of hassle at checkpoints.
As there were a lot of changes in the laws in the last years controls on trailers and trains are common and strict; it is all still confusing to people here so the uniforms know where to find income. I dont have to say that a US license plate might even be more magnetic to them.
Road taxes, vignets etc will be higher as you will pay for the trailer separately (also ferry costs etc)
To be honest, it is all achievable but you'll waste a lot of time and money on this. Why not ship the bikes over, buy a type approved trailer here and sell it on departure.
Good luck and if you would need help with something just send me a PM.