Since you haven't posted since the question was raised, you either solved the problem or have taken up knitting as a viable alternative.
For you (as well as others who might be reading this):
Are you sizing with gelatin or with acrylic? When I first experimented with gum, I tried acrylic sizing and just had no luck with it at all. The oil like spots you mentioned repeatedly appeared and I got generally poor adherence of the emulsion layer to the sized paper. I switched to gelatin sizing (30gm/liter hardened with 2 gms chrome alum). Every so often I experience a similar problem but that may be a function of humidity. Generally I find that the problem goes away when I do a smoothing pass over the emulsion layer with a dry brush.
I generally use two different emulsion layer mixes:
1) 1 part potassium dichromate (13%), 2 parts distilled water, 2 parts gum arabic with 1 part dry pigment mixed in 1/2 part gum arabic. Pigment amounts may vary depending. This is a fairly low contrast layer and gives thin color but for 3 part/four part color or even monochrome, its a good foundation
2) 1 part potassium dichromate (13%), 2 parts gum arabic, 1 part pigment mixed with 1/2 part gum arabic. This is usually a second pass mix for 3 and 4 color printing.
I apply with a soft foam brush, wait about 30 seconds them smooth out with a Liquitex synthetic bristle brush that's about 2 inches wide. Make sure the smoothing brush is dry.
Other factors to consider:
A particular batch of sizing was bad
Your gum arabic may be old or simply a bad batch
your watercolor may be a bad mix or old (I use dry pigments mixed on the spot)
The universe may just hate you that day.