To be honest I don't think that people back in the day actually cared about the razors in the same way we do today.
In any event, I have not had any direct experience with what you are asking. The only thing taping a spine really does at the edge is increase the angle (assuming any effects of the tape on the spine and hone nexus are negligible). So I suppose your question boils down to: are there razors that will not get sharp without increasing the bevel angle?
I think the answer would be "yes" to that. After all, razors have a geometry for a reason - the spine width to razor width ratio directly effects the bevel angle and I imagine that there is an optimal range for these angles - I believe there has been some work done in measuring these angles by numerous people. Two that immediately spring to mind are Randydance (I think) and mparker72 (also, I think). It may even be in the wiki somewhere.
But given tape has such a trivial effect on the razor angle, if you have a razor that seems to be effected by it that razor must really be operating at the margins, and I would suspect at the lower margin (flatter than the ideal range).
I guess that's kind of the theory from my perspective. However, there could be other things going on - multiple bevels being the first thing that pops into my mind: previous owner used tape, you've been trying to hone away at a flatter angle to what they did. Add 3 layers of tape - suddenly all is well? You said you have looked into it in detail, so that is probably not the case.
James.
2.
