Thank you for writing.
I would start with a soil test or at least a pH test.  You have been focusing on alkalizing the soil but I am not sure that will be productive.
The most common reason for moss is a damp shady environment of compacted soil that is seeded with a grass like bluegrass or rye that require a lot of sun. Moss does not kill grass but it moves into an area where the turf is weak.

Note last paragraph here. https://www.greenerblade.com/the-truth-about-shade-tolerant-grass-in-minnesota

Soil test http://soiltest.cfans.umn.edu/

https://web.extension.illinois.edu/lawntalk/weeds/solving_moss_problems_in_lawns.cfm  

Bottom line, after you have remediated drainage and compaction, consider a shade tolerant ground cover rather than grass. Flowing curved beds can add character to a lawn. Ginger, barrenwort, hosta, sedge,  

https://www.finegardening.com/article/10-ground-covers-for-shade

I hope this helps.