The 70mm difference between the forearm method and what you have is so large that the odds are good that the stem is too long. In addition 110mm seems literally a stretch for a 52cm bike. My experience has been that a very large proportion of bikes come with stems that are likely to be too long for the average person who would fit the bike. It may be due to the fact that a short stem does not look as "cool" or "racy."

I don't think it's possible with any method to get closer than about 10mm to the "correct" length for a given rider without in-person fitting followed by a tryout of the result. Whatever method you use, I would advise trying the result out with an adjustable stem that will allow you to vary things enough to find the just right length before going for the permanent one. If that is not available it is fairly easy to mount and remove a stem without any cosmetic damage, and exchange it for another until you find the right fit.

As stated before the handlebars can certainly affect which stem will work best. I changed my stock hb out to one that comes forward quite a bit more and that also has a significant drop. That results in a shorter stem than would want with bars that have a shorter throw and drop.

p.s Should go without saying but it's critical to get saddle height, fore-aft and tilt correct before judging stem and bar. The challenge is that how you feel on the saddle, rather than solely some formula, is part of the process and that of course can be influenced by stem and bars.