If you want to eliminate the transformer and the negative supply, and your load is high impedance (comparator input?), maybe you can use the circuit below.
Your original schematic implied that you already have an 8.5V peak sine wave. If you are actually getting the 8.5V sine from a transformer connected to the 120V mains, you can still use the schematic I posted. I am posting an alternate version that uses both phases out of the transformer. I show the option of getting your DC power directly from the transformer, which may or may not be useful.
Keep in mind that any of these schemes, including yours, will probably be susceptible to power line (mains) transients, but that may not cause a problem. Phase control, in fact, will tend to put transients on the AC line.