Unfortunately your electrician did you no favors.
Wiring from house to barn is too small hence the large voltage drop.
The power booster is increasing voltage too high----should only boost 10% so with 104V incoming should boost to 114V. Your booster is doing over 30% (104V to 138V)
YES that is too high of voltage. Surge protection will trip at 132V.
What brand/model of booster is being used???????
To resolve issue........
New proper sized wiring should be pulled from service panel to barn. THIS IS THE CORRECT WAY.
Otherwise you could replace the voltage booster (Unless it has just been set up incorrectly.....does not have variable boosting) with a Hughes Autoformer which just plugs into your 30A receptacle then you plug your RV power cord into it.
Boost voltage 10% when under 116V and only 2% when over 118V so that you get stable correct safe voltage
Hughes