I don't know that I can help you "prove" anything, but I spent about a half hour looking into this and can offer a guess about the situation. Bill Glowacki did indeed spend spring training of 1929 with the Phila. A's. He was not on their roster, so I assume he was a non-roster invitee. You are correct that he was then shipped out to Martinsburg of the Blue Ridge League. One article indicates that he played for Martinsburg, but he must have been in so few games that Baseball-Reference does not show him with the team. An article in the Mt. Carmel (PA) Item of May 3, 1929 indicates he had left the Martinsburg team the day before because he "found conditions unsatisfactory." He was going to return to Philly to meet with Connie Mack on May 20, but I'm not sure that ever happened. By June, he was playing something like semi-pro ball back around his home town again.
The only Glowacki in Baseball-Reference was an infielder in 1935, who seems to be a different player:
https://www.baseball-reference.com/r...d=glowac001---
Likewise, the Sporting News contract cards are not a source for him either. They have two Glowacki's in their files, but neither one is William "Bill" Glowacki.
https://digital.la84.org/digital/col...hterm/glowacki
My guess is that when the Obit said that William Glowacki posted with the A's in 1927, they were referring to his being with the A's in spring training in 1929. In my experience, the details in obituaries are often not reliable.
If you are looking for some kind of confirmation that he was or was not an actual major league player, you should be reasonably confident that he was not. Admittedly, research continues on who was or was not in the major leagues (and that's complicated even more if one gets into the issue of the era of the Negro Leagues now considered equivalent to the major leagues). But, for the most part, what was previously considered to be the inventory of 20,000+ major leaguers is pretty well established, and William Glowacki has not been among them.