If you have a condition that limits your shoulders flexibility, and you still can do a straight 5 x 5 of strict presses using 185 lbs, you could be a lot worse. This is very solid pressing for any drug-free lifter. It's just that our perceptions are skewed due to today's competitive landscape and a huge pool of talent, plus the game-changing use of PED's.
Of course, you're going to feel your press sucks when you compare yourself to the best pressers on the planet in today's world. If you wind the clock back several decades, you'll see a gold-medalist in the 1952 Olympic Games training the press by performing triples in the mid-200's at a bodyweight of around 200. http://ditillo2.blogspot.com/2012/09/no ... urray.html
. Doug Hepburn and Paul Anderson were outliers; most heavyweights were lucky if they could get to 300 in the Press (very strictly judged back then). When PED's became prevalent in the early 1960's, 300-lb pressers became common, with a big help from a quick loosening of the judging, which ended up killing this beautiful lift.
I take the time to write the above mostly for the sake of any novice lifter who might come across this thread. With all these monster shows of pressing floating around on YouTube, the drug-free lifter who finally manages to strict press 205 or 225 may feel quite discouraged, and not realize that this is a huge milestone for the vast majority of lifters out there. Most healthy men have what it takes to get to that level and more, but it usually takes a lot of work. Any sort of pressing for reps above 200 lbs is nothing to be ashamed of. Like you said yourself, numbers are irrelevent here.
Shoulder mobility is an issue I am totally unfamiliar with. My elbows and wrists tend to take a beating from volume accumulation, but my shoulders were never a problem. Yours weren't either until you developed that medical condition. I'm getting at an age where I start to value each year I go without any medical issue; health has become my #1 priority in the gym.
You said the log press is the least problematic lift for you. Getting access to a log would be a great addition to your training since this will be the most specific lift for Static Monsters anyway. (I didn't see any mention of a log press in your training log; sorry if I missed it.) Strict-pressing or push-pressing a log is certainly going to help with abs/core stability as well, especially if you hold your last set overhead for 10-30 sec.
Getting comfortable in the front rack position comes with practice. If you want to feel at home with a log in front of you, it is best to regularly practice with one. Some stretching may help if you feel stiff, but again, no one knows you better than yourself.