Pushbutton Servo Control with a 555

I've found numerous write-ups on getting a servo working with a 555 IC but it's not quite the functionality that I'm looking for. What I'm trying to do is have two buttons go to a predetermined position but the write-ups have two buttons that just go clockwise or counterclockwise. I know this can be done with an Arduino but I'm trying to avoid that route so I can keep the footprint as small as possible.

I've attached a picture of the schematic I was working from.

Picture of Pushbutton Servo Control with a 555

There are micro controllers as small and smaller than a 555 that can use Arduino for programming. So size shouldn't be an issue. You could get all the parts small enough that the buttons and the crystal will be the largest things on the board.

The problem with the 555 is it has no way of reading the signal line to tell what angle the servo is at. So you have no way of presetting an angle other than trying to time it out. So you know if you let it run for about half a second the servo will end up close to the angle you want kind of thing.

Sorry, you're missing the point about how the model servos work. They are given a position signal, and then drive to that position

A servo goes to the position defined by the input signal. If you mess about with the values of the resistors on the two switches, you'll be able to make it go to a defined position.