Yes, the 4060 (and 4020) do not output the first 3 bits.
To cascade binary counters, you would add on a 4040 or 4024. See the following link, 70% of the way down the page.
https://electronicsclub.info/cmos.htm
You are taking on a lot of work to make a 10 second timer with a resolution to 10 uSec.
If I needed to count time between shutter openings, I would photograph a stopwatch with resolution of 1/100 sec. An inexpensive digital watch has this function.
As for how to count time in 10 uSec intervals...
A cheap way would be to examine the binary pattern of led's attached to outputs of a 4060 IC (or rather two rows of led's, one at the top of the picture, another at the bottom).
Or if I wanted an easy-to-read numeric display, I would use an IC which drives a 3-digit counter (such as the 14553).
https://www.electroniq.net/other-projects/three-digit-counter-electronic-project.html
You would feed it a 100 kHz clock. Hence an increment of 1 on the display would be 10 uSec. It will take .01 sec to count to 999. Then it wraps around to 0 again.
You can cascade two 14553 to get more digits, or, there are 4-digit counter IC's.