Hi Alex
Just out of curiosity I read your posting on this forum and elsewhere. However I must say at this point that I have no intention of providing you with help via this forum due to the number of irrelevant and rubbish postings that are made. It is bad enough trying to provide remote help without the constant rubbish and nonsense posting that are made.
To possibly clarify the situation regarding the serial number. The first four digits of the serial number give the date that the design or revision was released to manufacturing not the date it was manufactured on. I would suspect that HP had problems with the manufacture of the CRT hence the delay in the scope being sold, CRT’s can have horrendous problems in manufacture.
As to a service manual, the copy on the Keysight web site is of a very poor quality and is almost unusable as are all of the copies on the internet. If you look at the 1982 HP catalogue (available on line) you will see an almost identical model to the 1727A, the 1743A, it appears the difference may just be the options fitted as standard. Artek Manuals have a high quality scan of the 1743A service manual available.
I would not be too concerned about the differences between the scope that you have and the service manual, rarely is an oscilloscope exactly as in the service manual.
The fact that the beam finder intermittently produces some form of trace is good news, at least most of the oscilloscope is basically working. What you need to do now is to check the oscilloscope section by section starting off with the low voltage power supplies and the voltages around the CRT only two of which are normally critical, the heater voltage and the pinch off voltage.
PLEASE take no notice of the multiple postings by one individual regarding CRT’s, there is NO understanding of how CRT’s work in them.
From what information you have provided I can see no reason that the oscilloscope cannot be repaired, my only caveat would be possible mechanical damage to the CRT internally, but this is unlikely and easily checked for..
G Edmonds