I too have spent a lot of time on my 7L5, mostly in a complete overhaul of the front panel hardware bits and correcting some assembly errors from the last person who took it apart. This hobby is at least as much about restoring these classic units as it is about using them.
Thanks for the links to your earlier posts. I had read them some time ago.
I can certainly agree that the "below 10 kHz" problem could be in either the 7L5 or the 7854. I will try to test my 7L5 in a non-7854 7k mainframe. I have an acquaintance locally who had at least one.
There is a big difference between the two problems, however. In the 10 kHz problem, the 7l5 is correctly tuned. Only the frequency display is wrong. In the power on problem, the 7L5 is actually tuned to 3778 kHz instead of zero. I can't think of any signals inbound from the 7854 to the 7L5 that can change the tuning. I still hope there may be a 7L5 solution to this one. I will keep searching.