The offset range is multiplied by the attenuation before the offset signal is added. In the Rigol 1000Z series, there is only one switchable x100 attenuation stage yielding two offset ranges. Further, the dynamic range of the 1000Z input amplifiers is small limiting the range of the offset signal.
Some old analog oscilloscopes have huge offset ranges. A Tektronix 100 MHz 7A13 supports +/- 10 volts of offset at 1mV/div and +/- 100 volts of offset at 10mV/div. It is like having a position control with 10,000 vertical divisions of range but these were not primarily designed for this reason. What they allow is "slideback" precision DC voltage measurements at any point of a waveform using an analog oscilloscope. This is why the 7A13 is called a differential comparator and not a differential amplifier although it does that as well.
The modern implementation of the Tektronix 7A13 is the Preamble Instruments 1855 and from what I remember, the same designer worked on both. Preamble was bought by LeCroy but still produce this stand alone differential probe amplifier. If you have to ask the price, then you cannot afford it.
As far as the x1 versus x10 passive probe, the output impedance of a power supply or regulator is so low that the added capacitance of the x1 probe is insignificant but its relatively low bandwidth limitations still apply.