I, like many of us here, have extensive practice at using the halfswording techniques from our source material with a variety of
sharp blade forms, and I can attest, as can they, that it works just fine (that is not to say that you shouldn't be careful when trying it for the first time).
As for grabbing the blade towards the point, that is particularly easy to do with a bastard or very tapered sword, as it allows a firm grip all around the narrow blade.
I also don't believe in differential sharpening. That's something for blades of uniform thickness. The blades of medieval and renaissance europe had different cross sections at different portions of the blade, and each portion of the blade was as sharp as that cross section would reasonably allow.
Master Vadi, for one, mentions differential sharpening, i.e. he says that a certain blade form should be sharp a hands length from the point, but then goes on to show the weapon of which he speaks is only capable of an edge there due to it's blade geometry.
But our source material even shows halfswording techniques with wide bladed messers or falchions; weapons with the sole intent of the blade form to lend maximum sharpness and cutting ability vs. unarmoured opponents; and it's being done safely and effectively by expert fighters.
I wouldn't say "trust me" in martial arts often, but from all of our testing and practical application, and the unquestionable ubiquitousness of such techniques in our tremendous amount of source material which was unquestionably written by experts in the arts of killing who trained with such veracity and pragmatism, and our hands on experience with a variety of antique and accurate replica weapons, it's probably one of those things I'd say you can have some blind faith in and work towards until you "get it."
...or if it is a regular technique which can be performed with confidence and strength while grasping a blunter blade firmly.
It is a specialised but common technique which can be performed with confidence and strength while grasping a sharp blade firmly. There are no "just so" grips in life or death combat, and firm grip is what keeps your hand in one place and one piece. You have to halfsword like you mean it.