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Well, the first thing I would suggest would be to increase the bootstrap capacitors E9 and E10 from 10uF to 33uF.
Feed the 555 output to a flip flop. Feedback the outputs of the flip flop a high/low side driver which will drive the four MOSFETs in the H-brigde.
Why do you want to use the 555 chip? Can't you use SG3525 or SG3524 or TL494? Or even the CD4047?