The only thing you can change with the software is the DC offset going into the ADC by varying the bias of the op-amp that drives it. This is what you do when you change the Ypos control. However, this is only limited to the height of the screen. When you have a DC level at the input that moves the signal up above the top of the screen, you will be clipping, thus losing the signal in the PREVIOUS op-amp that drives the ADC section.
So nothing you can do around the last op-amp/ADC section (which is the only access point for the software) will help because the signal will have been lost in the previous stage, clipped to either the power supply rail or ground, depending on the polarity of the DC offset.
The solution is to inject a DC current at the INPUT of the first op-amp, balancing and “neutralizing” the DC offset at the input, so that the first op-amp doesn’t “see” this large DC offset, restoring the signal position to within the screen.
This could be done by adding a PWM output from the microprocessor, filtering it into a DC level, then feeding it to the INPUT stage, like the one at the output does now to adjust the waveform’s vertical position. This is essentially the difference between position controls and DC offset controls. The position controls adjust the signal at the ADC input, while the DC offset controls balance out the DC at the input of the first stage, before it can get amplified and cause mayhem by overloading subsequent stages. Remember that the preamp stages in these things only run at 3 or 4 volts, giving a +/- 1.5 V range, barely enough to clear the top/bottom of the screen. Special op-amps, so called “rail to rail” needed to be used to operate within such a narrow window.
So to implement this properly, you would need to have a spare PWM port available from the processor, construct the proper connections and filter network on the circuit board, and add the proper software function to adjust this, along with some display for the compensating voltage value. An additional series of steps to calibrate this would likely be needed in the calibration routine. Also, careful attention would need to be given as to exactly where and how this is injected at the input so as to not disrupt the attenuator calibration for the various ranges.