Perhaps this is why Ansel suggests making your own grey card? It is not the exact 18% grey reflectance that is important but the way the notional tone affects the rest of the processing chain. So you make a Zone V grey card to suit your meter.
If the reflected light meter is calibrated for a K14 and the incident light meter with a flat receptor is calibrated for C250 then a 17.59% gray card should give identical reading. Meters are calibrated for K12 to K14 often. But I don't know about the Weston it seems 1 stop is a lot.
Why don't reflective meter reading of zone V card and an incident reading match?
I understand that the selenium cells in meters like the Weston series do deteriorate. I have a Master IV in beautiful cosmetic condition, but the readings are useless. It used to be possible to have the cell replaced, but it would be cheaper to get a more recent version second-hand. I have to say that I also see differences between readings with incident and reflected measurements.
The selenium cell, if it is un-damaged, can last a very long time.
I have a Master II which gives reasonable readings, but have had a couple Westons that didn't work as well. In general I find they are fully good or totally bad (though the problem can be loose connections).
I think the Weston series of meters are "pretty well" designed, as far as protecting the selenium cell goes.
You might need to get in the habit of using Tungsten speed ratings that are lower than Daylight speed ratings. Sensitivity of selenium cell to near infra-red makes the needle jump higher under Tungsten than it should.
By the way 1 stop higher reading of 18% gray card seems perfectly reasonable.
I accidentally did an 18% gray card exposure test, so here is the graph...
Basically the lowest diamond on the lower-left of the curve is 2 1/3 stop below 18%. (18% is the middle of the cluster of diamonds mid-curve). Imagine that lowest diamond is about Zone III. Really would have rather placed Zone II down that far on the curve. So one stop more would have been a better exposure.