Thanks for the photo. Mine are done the same way, I just didn't think the design could be described as grommets since they are integrated in the elastic suspension. Yes, my motors too can wiggle, and they're silent to the ear, with just a faint 100 Hz hum that can be heard by solidian transmission (ie. through a stethoscope). It took some time to solve a faint grinding noise on one motor, the other one has always been this quiet, which is fairly impressive for a machine of this age.
In fact the deck appears mostly silent when you listen to it, it's only when you listen to a record that the hum transmitted to the cartridge appears and can be annoying in the quiet moments. I know my ear is easily disturbed by artefacts, but in a previous thread on the topic I exchanged files with another 1019 owner and it appeared that mine are distinctly noisier than others, although even those have the dread 100 Hz buzz too. Indeed the stethoscope reveals a loudish 100 Hz buzz in some areas of the chassis, in particular around the speed control assembly and the base of the tonearm, whereas other areas are practically silent.
At a point I solved the problem by using an external tonearm, ie. based out of the chassis. That reduced noticeably the hum, but not nearly enough to compete with the 1229 which is also an idler with a heavy platter, high PRAT factor and all. Besides the external tonearm was cumbersome, so I eventually just gave up on the 1019. I came to wonder whether the sound that makes the 1019 so desirable is not precisely due this 100 Hz tone, and when I filtered it out electronically I found the resulting sound very similar to the 1229, but that's just a subjective impression, not evidence. Maybe I just dislike what others like, I don't know. Or maybe I'm just listening to the wrong kind of music for the 1019: I try it with classic and its inevitable quiet passages, whereas variety / pop would not allow the problem to appear? I don't know.