Dear Martin,
I'm afraid I'd have to disagree.
Note, for example, that the Ames Model 1832 short sword that Glen posted is lenticular where fullers are not present: by the guard, above the double-fullered section of the blade; between the double-fullered and single-fullered sections; and below the single-fullered section, at the tip. I know that the sword itself isn't relevant to your request in this thread because you specified that you are not interested in short swords, but it's a good illustration of the matter at hand.
Addressing your other argument, you say that a single-fullered sword must be of its nature hexagonal, not lenticular. But this need not be true if the blade's longitudinal sections between the edges of the fuller and the edges of the blade (I avoid the term "flats" for obvious reasons) are convexly curved. If they are flat, then yes, the sword is fundamentally hexagonal; but I don't think that it's accurate to say that "in the forging process these swords are closer to hexagonal cross sectioned". As an example, a blade could be forged with a lenticular
cross-section before the fuller is either forged or ground (or forged and ground) in. I don't think that you can use the shape of the blade during forging as a criterion anyway, because at some point it's very likely to be oblong in cross-section. That doesn't affect the blade's final cross-section, but is a more or less unavoidable artifact of the forging process: A bar is drawn out from a billet, or blanks are cut from a matrix. No sword can be said to have a particular cross-section before it's finished, because both forging and grinding are part of the production process for all traditional swords. (One might choose to say that swords shaped entirely by grinding don't conform to this rule, but those would be rare historically; and I'd disagree with that assertion anyway, as follows.) There are some situations in which a sword's cross-section may change after its initial manufacture, but then I think that we have to talk about the sword as it was first made and as it was later altered. The sword is not somehow both or neither, nor would it be "not really" of the final cross-section merely because at some point it had been of a different cross-section. It is what it is at the time that it's examined.
These arguments, of course, omit cases of multiple cross-sections in the same blade, which are certainly possible. But in such cases, we can only talk about the cross-sections at particular locations on the blade, echoing the argument above.
I hope this proves helpful.
Best,
Mark Millman