Spending two days in a lab can easily save you up to one hour reading literature

This is a canned comment to let you know that it looks like you're trying to implement something that is non-trivial with the power-hungry NE555 but is very easy for someone using a microcontroller.

This is just a canned comment to let you know that what you're trying to build from discrete analog components (possibly incorporating Opamps and/or NE555) is a digital control problem and thus can easily and with lower parts count be solved with a microcontroller with really minimal firmware to write.