A 555 pin 3 output never is a sawtooth waveform. A pseudo-sawtooth waveform appears at the top of the timing capacitor at pin 2, but it actually is a portion of the standard exponential charge/discharge waveform of an R-C network.
There is a more simple 555 astable circuit that gives nearly 50/50 duty cycle with fewer parts.
One way to clean up your circuit is to use this circuit for both U1 and U2. To make U2 change frequencies, have U1 switch in and out an additional timing capacitor rather than an additional timing resistor. This will take one diode.
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There is a more simple 555 astable circuit that gives nearly 50/50 duty cycle with fewer parts.
One way to clean up your circuit is to use this circuit for both U1 and U2. To make U2 change frequencies, have U1 switch in and out an additional timing capacitor rather than an additional timing resistor. This will take one diode.
ak