Could you use a digital up/down counter (direction switches at end of sweep) with a DAC, running from a higher frequency oscillator? An 8 bit DAC would use an input frequency of 1024Hz to 16Hz. A higher resolution DAC would require faster clocks (12 bit would be 16kHz to 256Hz.
Two options for controlling the rise/fall times:
1- Make the oscillator frequency variable.
2- Run from an even higher frequency, and use a counter with reset to divide the frequency down to the frequency needed for the DAC steps.