60V Hot to onward neutral
When you 


  disconnected all of the neutral wires.


You changed the configuration of the circuit. Basically all circuits in the US are wired in parallel. When you disconnected the neutrals you change that circuit into a series or combination series/parallel circuit. The only thing you are reading by testing the hot circuit against the two disconnected neutrals you show in you drawing, is whether or not it is an open circuit or there is still a connected load on the circuit. So if you are reading 60V it could be a phantom voltage or it could be the the series reading of the drop across you meter. That means if you touch it you will find out why we call it a series neutral since it will shock you.

You question isn't clear about what you were testing the circuit for other than you stated you were testing for voltage drop. If you are trying to test for voltage drop then you are doing it all wrong. Voltage drop is directly proportional to the load of a circuit. That means you have to have a load in the  circuit to determine your voltage drop. 

Let's say you have a motor at the end of your circuit. In order to find the true voltage drop for the motor, it should be running at full load. Then you would take the measure the voltage at the breaker to the neutral (let's say it's 126V) then take another reading at the motor connection point (say it's at 122V). Then you know you have a drop of 4V between the breaker and the load. 

Because you are exposing yourself to live electricity, it is difficult to measure equipment while it is running. In order to determine voltage drop in most cases we perform a voltage drop calculation.

Point being when you disconnect all of the neutrals, you will get all kinds of strange readings that really don't mean anything relevant to the complete, operating electrical circuit.

Hope this helps.