That makes sense. I guess that could be the reason that my gums are all puffy and bleeding.

Puffy and bleeding gums can be from bacterial infection or simply a lack of vitamin C.  This is why these are symptoms of scurvy.  Keep in mind that the adrenals get priority over available vitamin C in the body followed by the retina and brain.  Other parts of the body get what is left over.  If we stress our adrenals this increases the requirement of vitamin C by the adrenals, preventing more vitamin C from reaching other tissues.  Just look at how fast meth addicts age and lose their teeth.  They are serious taxing their adrenals leading to lowered levels of vitamin C in most of the tissues, which in turn leads to a loss of structural proteins.  

Try to get most if not all your vitamin C from natural sources.  The best sources include papaya, kiwis, berries, watercress, nettle leaf, amla, acerola cherry and rosehips.  Watercress and nettle leaf also help due to their silica and rutin contents that help to strengthen blood vessels.

Can I chew on some licorice root or do I need to take it in a capsule?

Chewing it or making a tea by boiling it would be best since it is also antibacterial.  If you make the tea you can swish it around in your mouth before swallowing it.

I'm working with Dr Lam and we are in the process of weaning me off of glandulars so I'm fearful of adding anything new, but I would be more inclined if chewing on it would be beneficial to my gums and not be too stimulating.

Use Chinese licorice root (G. uralensis), which is more calming.  American licorice root (G. glabra) is slightly stimulating.

I like kefir for a probiotic, but it is going to contain acids as well.  The other  way is to skip the probiotics and focus on prebiotics instead to help stimulate the growth of the flora.  My favorites are rice bran and oat bran but chickweed, Jerusalem artichoke, gums (guar, konjac, xathan, etc.) and chicory root  are also very good.