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...Do you need the pulse to the motor?
...Will it not start on the lower speed settings?
Ahhh. Remove the cap from pin 5 of the 555.
I've used this https://www.jameco.com/webapp/wcs/stores/servlet/Product_10001_10001_120539_-1 kit and was very happy with it. Is it an almost ready made solution for you?
I thought the PWM thing actually worked?
OK! 2 seconds is a long time for a power on reset signal. I spent a long time getting an elegant delay design to work. You didn't buy and J174 Fets did you? I have an idea that should work on power up, but once it has been running all bets are off because the reset time would be long. The 555, in my opinion, is glitchy on power up especially if you want it to "one-shot" type things.
Sorry, I'm to old to wait for that simulation to finish.
So I ran it in Spice. The only thing I see is that the 10K on the base of the 2N2222 should be between the base and the output of the 555.
Remove the cap on pin 5 and use the 220 Ufd as the power on reset cap (In place of the 47Ufd.) It simulates a ok now. I'm not sure of the condition of the 2N2222, but probably ok.
Congratulations! You did most of the work.
Did you try both output circuits (Transistor based H-bridge, SSR based H-Bridge)?