Drover,
Yes, you can reprocess the poorly converted batch.
Providing the batch has not been left open and has lost most of the methanol, you can reprocess with minimal methanol added. If you have lost methanol, determine the current batch volume compared to the initial batch volume (the difference will be the methanol volume lost) this amount of methanol will need to be added back to the batch for reprocessing.

I believe that it is not necessary to separate off the byproduct to reprocess, but you should take precautions to minimise methanol loss (this will need to be added back if the reprocess is to result in good conversion).
Take well remixed 1 litre samples of the biodiesel and byproduct and add some caustic in methanol to re-process.

Here is my suggestion:
Use 100mL of methanol and dissolve 10g of caustic in it (I think that this is not too much to fully dissolve). This makes a concentrated solution, of which 10mL will contain 1g of caustic.

To 3, one litre samples at 50°C, add 1, 1.5 and 2 mL respectively of this concentrate and agitate for 20 - 60 minues. (if methanol loss is significant, you will need to add back the lost methanol volume)
When the separation is complete, perform a 3/27 test on the biodiesel from each and determine the lowest amount of added caustic which results in good conversion.

Multiply this up for the batch oil volume (minus the test litres), dissolve in the smallest amount of methanol possible, add any lost methanol and reprocess the batch. This allows the methanol which is still in the procesoser (in the byproduct layer) to be used in the reprocessing of the batch.

Please report back to the forum on the success or otherwise of this suggested process, as others could benefit if you have success with it.

The alternative, after removing the byproduct will require much more methanol to be added.