If you have merely netralised the FFA and had little to no transesterification then you will have produced soap but little to no glycerol. The soap is normally present largely in the glycerol, so with no glycerol present it will be largely in the oil which could result why you appear to have a thick paste. The low temperature will make the paste appear thicker especially if near the gel point of the oil.
Adding the aditional methanol could have helped thin things down slightly, but bearing in mind that the veg oil is not miscible with methanol, the top layer could be largely methanol with whatever would dissolve in it, any thing that has transesterified, impurities that would normally be in the glycerol, and glycerol itself in the methanol.
The second stage should result in transesterification moving much further along and glycerol dropping out.
You could try adding only have the amount of caustic you were planning for your second stage which should result in significant reaction but is unlikley to get anywhere near complete, but should result in some glycerol dropout.