That page includes some Rogers numbers near the bottom of the page, but they don't help. I'm not sure that Grotrian Steinweg were involved in any way other than retailing them, and plenty of Reisbach pianos were sold by other people. The number preceded by A is unlikely to be a serial number. The other number is too short for most serial numbers, and neither corresponds to sequences for Rogers or Grotrian, but a lower number might indicate a new sequence for these, in which case I have no dates.
I have tuned a few Reisbach pianos by Rogers, but I believe they used the same number sequence as the other Rogers pianos, so I just ignored the name on the front. Perhaps your piano has a longer number hidden away somewhere. The last 3 digits of this may be imprinted on removable wooden parts such as the music desk.
The best hope is that the action (the working parts of the notes) may be marked with the action makers’ name and number, and we may be able to date this. (If it's a Herrburger Brooks action, we can only say it is after 1919.) However, removing the action can be risky in an old piano, and you may need your tuner’s help.
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If you find old references or links on this site to pianogen.org, they should refer to pianohistory.info