I don't know where you are looking to measure 60V, but for measuring a high impedance source you can use the opposition method, where you arrange a controlled voltage supply and a current meter, you put the current meter between the measuring point and your well known voltage source, which is low impedance, look for zero current, then you measure the voltage of your low impedance voltage source, which may be a 70V PS and a 50k pot, which is low enough for a DMM to measure directly, that way you get rid of the insertion error by loading your high impedance source, since you are measuring at zero current.
For the transformer I would start measuring continuity, if there is some you are good, but it still could be shorted, if you have a L meter could be useful to know the value outside the circuit, in which case, if it's roughly close to expected no shorted windings, if you have shorted windings inductance will be really low, some mH or less, depending on the windings, someone who knows the transformer we are talking about may give you some better approximation... If you don't have an L meter you could shot some signal to it and see what happens at the other side, or measure inductance with a signal generator and a DMM with a series resistor.
JS