From observation, it appears 240 x 64 pixel LCD modules have more or less standardized on two sizes:
Most of the 240x64 pixel displays are based on the T6963 or equivalent RA6963 controller . The vast majority of these are 180mm x 65mm in size. A notable exception is an RA6963 based range from Newhaven Display, which measures only 118mm x 45mm.
T6963/RA6963 based modules have their controller on the LCD's PCB and is referred to as Chip On Board (COB) modules.
A more recent alternative is to integrate the controller and associated electronics onto the LCD glass, resulting in more compact designs. Controller On Glass (COG) displays do not require a PCB as part of the module, but it is often included to simplify connections and mounting.
COG type LCD modules tend to be smaller, measuring around 120mm x 45mm or less.
At 166mm x 55mm, the LCM24064YGF's lands somewhere in the middle.
Though the smaller modules could be made to fit, filling less than two thirds of the display area would be less than ideal.
The size of larger modules could potentially be reduced by trimming their PCB (at the risk of impacting circuitry).
Worth a mention is the HG2406411G-VA , which is the only module I came across which actually matches the dimensions of the LCM24064YGF. It is available through Alibaba, but with a minimum order quantity of 1000 units.
Since there is little chance of obtaining a controller-less LCD module, it can be assumed that an interface will be required to connect the replacement to the Z1's controller. Let us further assume the interface could be made to work with whichever controller the replacement has.
That leaves the main criteria for a replacement as:
The stated criteria are met by the Surenoo 24064COG-40 Display from AliExpress.
The replacement's display area compares well with the original. The PCB is too big to fit, but since it is a COG type display, the PCB is only sparsely populated with lots of potential for trimming without impacting vital circuitry.
At US$15.80 it happens to be one of the cheapest 240 x 64 LCD displays currently available from AliExpress.
There does not appear to be overly much information available on the Surenoo 24064COG-40.
The following was gathered from different sites, with help from Google Translate.
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