That is my understanding, also. Greeting "ohayou gozaimasu" when showing up to work regardless of the time of the day was done by people in "mizuchoubai." People in "mizushoubai" did not start work till later in the day. Then people in the entertainment industry picked up the habit of greeting "ohayo gozaimasu" when showing up for work regardless of the time of the day. In Japan, the entertainment industry is also considered as "mizushoubai."

The general public in Japan, I think it was the young generation who first started to greet "ohayo gozaimasu" when showing up regardless of the time of the day. The young generation was mimicking what they saw celebrities doing on the TV or radio. This was how many decades ago...? Back at that time, adults would look at that as young kids not knowing manners and don't know proper Japanese. But now this has spread to middle age and elderly groups, especially in the workplace. But outside of the workplace, especially with people not familiar, it is still time defined greetings; ohayou gozaimasu for mornings, kon-nichiwa for afternoons, and konbanwa, for evenings.

As for 25:00 (not 01:00 or 1:00 a,m,), I looked up, and seems like this was started by newspapers. Before the Internet, TV and radio schedules were printed in newspapers (newspapers still do) in Japan. Japan did not have a TV Guide (not in '60s and '70s). I vaguely remember the TV Guide was introduced in Japan in the late '80s or somewhere around that time. Anyway, starting in the late '60s and '70s, TV stations and radio stations in Japan started to broadcast late at night, beyond 12 midnight. Newspapers started to use 25:00-26:00 on TV and radio schedules. Yes, there are no standard rules regarding the format of the 25:00 type time display. One piece of information I found suggested the use of the 25:00 format became more widespread during the bubble economy era of Japan (1986-1991). During the bubble era, many businesses in Japan extended their business hours, izakaya, conbimi, family restaurants, etc. which led to 24 hrs. operations.

As for the use of 24 hrs. system in Japan, it was the railway company started to use 24 hrs. system. Japan National Railways (predecessor of JR) used to have a lot of long distance trains that ran day and night, including local trains which stopped at every station. JNR had long distance local service which ran Ueno (Tokyo)-Sendai, Ueno-Niigata, Tokyo -Osaka, etc. To avoid confusion about departure and arrival times, JNR started to use 24 hrs. system, and the use of 24 hrs. system spread in Japan.