At least it's nice and modular, no nasty flex-prints.
I Just noticed that the manual I linked is for the 4660M so the driver chip could be different (irrc, the HD44780U is a dot matrix driver) but I'm not clear on the two DMM models / variants.
It's certainly worth checking for bad solder joints - I notice that there's a Zener too... worth monitoring.
Worst case, yes, you can replace the blob with the appropriate IC on the pinout. Just a warning though that the epoxy is really tough, you'd almost certainly need to desolder the LCD before you could safely attack it.