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Hello,
I would recommend against using a monostable multivibrator for any type of precision timing. If you're ok with up to ~50% variation, then that's an application I would recommend this type of device for. You can technically get better timing accuracy than that with good external components, but the device itself still adds up to ~3% of variation from just temperature variations, and then you can get changes from supply fluctuation and process variations as well.
If you're set on using this device, I would recommend going with a smaller resistor. Large resistors create a voltage drop when leakage current is high, and thus can cause inaccuracy. Generally speaking, it's best to keep the resistor between about 3k and 300k. By increasing the capacitor 1 order of magnitude, you can decrease the resistor to a smaller value (about 100k).
It sounds like you're working with a real device in a lab already, which is the best way to test for component values with this type of timing component. Simulations and formulas can only get you so far -- you really need to build the circuit to know how it's going to perform.
Please note that even if one device does exactly what you want, when you build the same circuit with another, you will likely see some variation.