THRUTRAFFIC--
First, I have to say that I haven't had occasion to try to track this type issue in my 2552; AC supply has always been fine. Therefore, I don't even know how much (if any) voltage drop I get (shore power or generator) with a NORMAL system when applying a heavy load such as A/C or microwave. That would be good to know. However, 3 volts with a toaster or 5 volts with a 15-amp load that you mentioned definitely sound excessive.
Excessive voltage drop usually comes from one of two things--either there is a high-resistance connection somewhere in the line dropping the voltage, or something in the circuit is pulling too much current dropping the voltage. The difference is that if something is pulling too much current, the voltage drop will show up all the way back to the voltage source (transfer switch output in this case). If there is a high resistance connection, voltage on the supply side of that connection will be normal, but voltage on the load side of the resistance will drop low.
I would check voltage at the output of your transfer switch (ideally on both external and generator power). If it holds relatively normal there when you apply a load, the problem is downstream--probably a high resistance connection somewhere in the main feed wire. However if it drops there when you apply the load, check the inputs to the transfer switch;. if it drops there check back toward the actual inputs to the coach (at the generator and main cable connector). Since you said you found no issues under load at the lot power, if you've got a drop at the transfer switch output--the problem has to be somewhere between the two. The Klein Tools CL380 is a 400 amp meter, so you should be able to check (again at the transfer switch) for excessive current going somewhere with no actual load that you've applied. That's probably not a high percentage problem, but not impossible.
Mike