Carl,
I'm not sure what is causing the offset; try placing a 1kR resistor to ground on the non-inverting input and check that both diodes are reasonably matched zeners. How are the offset pins on the op-amp connected?
If the zener diodes are perfect (they aren't, not even close) then the output voltage of this circuit will be:
Vo = 11 * Vin | small Vin, that is |Vin| <= (Vf + Vr) / 10
Vo = Vin + Vf + Vr | large Vin, |Vo| < maxVo
Vo = +- maxVo | when the opamp is at it's limit
where:
Vo : output voltage,
Vin : input voltage,
Vf: diode forward voltage ~= 0,7V,
Vr: diode reverse voltage ~= 5.0,
maxVo: maximum output voltage of the op-amp at the current supply voltage and output current.
When this circuit is "clipping" at Vr + Vf the output will still have a term equal to the input as the feedback loop drives the inverting input to match the non-inverting input. So in the perfect case this circuit will still have a hump when it clips.
The zeners will not be perfect and you should look at the datasheet for the relationship between current and voltage around the knee (or measure for yourself). This will round off your corners.
Perhaps the biggest problem is the lack of headroom. The 741 output limits several volts below it's power rail (this is dependent on the output current). With +-9V power rails and a circuit configuration that will only clip at Vo >= 6.2V the circuit may limit due to the op-amp before the zeners start limiting. You could try higher voltage power rails. It's worth pointing out that the 741 is obsolete in term's of it's performance; these days you can get better op-amps for the price of the package they come in.
P.S. The datasheet for a 741 I have (Texas Instruments LM741 SNOSC25D – MAY 1998 – REVISED OCTOBER 2015) recommends a minimum supply voltage of +-10V!. Look through your datasheet for "Recommended Operating Conditions" and "Output voltage swing."