True. I don't think the chubby cheeks are the real problem neither. I agree there seems to be lack of vertical length.
I think the OP (tim) has to isolate his problem(s), one at a time in terms of what bothers him more.
Like if the cheeks are truly chubby, trying to 'hide' that with FILLER to the jaw line can just result in a bulked out or CHUBBY jaw line where you're not really 'hiding' anything but rather MATCHING it up with another area that can be 'CHUBBED out'. Although fillers can be used to augment jaw line, they lose their 'sharpness' over time where they just end up looking BULKY. So, matching chub with MORE chub somewhere else just creates look of overall chub or bulk.
ISOLATION involves tackling ONE area at a time. So, if his cheeks bother him more and if they are really chubby, he can look into fat reduction modalities to reduce the chub providing of course, the chub is FAT they can target with what ever procedures they target fat with. (His homework to look into that. Not mine to list each possible one.)
Jaw area has little to do with his chubby cheeks or just just say the perception of how the cheeks look. Although jaw area is an area that could be made better IN IT'S OWN RIGHT and he could probably get a nice jaw line area with well selected implants, doing so isn't going to make his chubby cheeks 'go away' even VISUALLY. Well articulated or 'robust' jaw lines just FRAME the rest of the face. So it depends what they are framing.
As to lack of vertical length, IF what is meant is length to
the chin area, consider that in a sliding genio vertical length is LOST and horizontal advancement is GAINED.