JerinG, Welcome to engine design where ideal calculations alone aren't sufficient. That doesn't mean, however, that we should use the
wrong calculation just because it seems closer to empirical results!
The theoretical isentropic calculations don't include port flow (volumetric efficiency), impacts of valve timing, heat transfer, or compression leakage (aka dynamic compression effects). Once properly adjusted for these factors, I assure you it would match your empirical expectation (assuming those expectations are correct... see "by the way" below). It is a dangerous design error to use an isothermal (constant temperature) calculation as gasses under compression
do in fact increase in temperature (otherwise a diesel wouldn't work). Your isothermal calculation only
appears correct because its errors are (apparently) roughly equal to the losses that aren't accounted for in the theoretical isentropic calculation. That's merely a coincidence. Read the references I provided.
By the way,
this article shows the BMW R1100GS also has a 10.3:1 compression ratio, and
this video of an R1100GS compression test shows 200 psi (13.8 bar). That's 40% higher than your expectation.
P.S. We don't actually use the isentropic calculations for engine modelling; they're used for approximations. Instead, we use PV=mRT where P is in Pascals, V is in cubic meters, m is air mass in kilograms, R (the specific gas constant) is 287, and T is in Kelvin. We break each cycle into very fine time steps and keep track of mass transfer, heat transfer, and volume then calculate pressure. The mass calculation does use a typical value for lost mass during compression and expansion that no doubt approximates the 8% to 12% loss of compression pressure (I plan to check this just to satisfy my curiosity).