I haven't seen anyone mention formatting their card as exFat.
The fastest startup time I was able to achieve, from turning the camera on to being able to make an image with the M262, was 1.6 seconds. That was with a Panasonic Gold 8GB card.
Time of other cards I tested:
16GB Sandisk Extreme Pro (95MB/s): 1.8 seconds
16GB Panasonic Gold: 1.9 seconds
16GB Samsung Pro (white card): 1.75 seconds
In order to measure the time I turned on the camera while holding down the shutter button. I recorded this on video. The audio was imported into Audacity, which allowed me to "see" the sound of the on switch and end with the sound of the shutter opening. The audio spikes in Audacity allowed for a precise measurement.
Formatting the SD Card as exFat is the key. I also tried SD Card Formatter alone and in conjunction with formatting in the camera. That didn’t seem to make any difference. Once I formatted the cards as exFat I recorded my fastest start-to-shoot times. The 16GB Panasonic’s start-to-shoot time when the card was formatted only in the camera at the card's default MSDOS FAT format was 5.2 seconds. Formatting the card first in my computer as exFAT, then formatting the card in the camera reduced the startup time on this card to 1.9 seconds.
Try it on your M240's and see if the startup to shoot times drop below 2 seconds.