Could you make a guess as to whether shipping ethanol from Brazil would level the EROEI? How about the cost?

Don't know the exact numbers, but shipping LNG uses 6-15% of it's cargo to ship to the U.S., depending on the length of the trip.

I'm guessing it would be in that range.

Wouldn't ethanol be a lot easier to ship than natural gas?
LNG has a uniquely high transportation loss due to boil off from the cryogenic LNG storage tanks.  Because they know that they will be getting lots of "free fuel" on the cargo run, ship designers build LNG carriers for speed (less evaporative loss) and not low specific fuel consumption.

This puts the US at a disadvantage in importing LNG.  For all the LNG exporters, the United States is the closest market only for Trinidad & Tobago.  Nigeria is closer to the EU, Qatar, Iran & Australia are closer to Japan & China (that will be a LONG haul to the US !), Western Russia is closer to the EU and Eastern Russia to China & Japan.  Mexico is the closest market for Ecuador.

The larger oil tankers are, the more efficient they are due to the cube/square law.  I would suspect that <1% of the fuel is used for transport of Persian Gulf fuel to the US.

Thanks for this information, Alan. This was news to me.
Do the LNG ships use the boiling off gaseous fuel for power? That is, do they take the gas as it boils off to power the ship or at least power the generators? If not, what a waste.

You can reduce boil-off of course by better insulation or take boil-off to power refrigeration equipment. (or both) In any case, it's some mighty cold stuff to have to ship. It would be better to turn the gas into gasoline then put it in a tanker at the source, saving the energy to refrigerate it. Of course, that doesn't help our NG woes.

They use the no longer L NG as fuel.  AFAIK, they pull with a full cargo on oil and then add NG as it boils off.  By the end of a long voyage, they have too much free fuel to use.

Thicker insulation means less LNG (inside diameter shrinks as walls get thicker).  The whole purpose is to deliver NG and the optimum point is found in design.

Note that the "optimum point" for Nigeria to Spain is quite different than for Qatar to East or West Coast US (thicker for US I guess).  So misusing a thinner insulation LNG designed for shorter hauls for Qatar to US will deliver a bit less than designed.