The right pH for my moss

OK, let us start with moss... How should I tweak my environment to make it good for moss and bad for grass?

Collective internet wisdom says that typical moss likes:

• moisture
• shadow
• compact soil
• acidic soil (about 5.5pH)

I believe that the mossy area of my lawn has the first three characteristics.

This last point makes me nervous - according to my measurement, my soil is neutral - around 7pH. Either my measurement was incorrect, or I have a kind of moss that likes neutral acidity (or at least other factors overweigh the lack of acidity).

To measure the acidity of my soil I bought a cheap "HoldAll by AmerTac" soil meter at my local HomeDepot:

 

It measures pH, light level, and moisture level. It is too cheap to be real, but I measured some trivial items (tap water, then tap water after adding several drops of lime juice) and it seems to work. Probably I should have chosen a chemical test kit instead, but for now I will assume that my pH meter works.

I have no clue what kind of moss I have. Here is a close-up (click to enlarge):

 

Ideas, anyone?

Just in case, I'll make my soil more acidic - unless I have some weird kind of moss, more acidic soil should make it happier, plus it should make the remnants of the grass suffer, which is exactly what I need.

Today I spread two 2.5lb bags of Encap's Fast Acting Sulfur over the area I plan for moss. Hopefully it will lower the acidity by 1-1.5 pH within few weeks.