Wireless systems with inband full-duplex transceiver typically require multiple lines of defense against the effect of harsh self-interference, specifically, to avoid saturation of the analog-to-digital converter (ADC) in the receiver. We may unite the typical tandem operation of successive analog and digital self-interference cancellation (SIC) stages by means of digitally-assisted analog SIC. In this case, the ADC in the receive path requires considerable attention due its possibly overloaded operation outside the intended range. Using neural-network-based architectures of the transmitter nonlinearity, we therefore describe and compare four system options for SIC model optimization with different treatment of the receiver ADC in the learning process. We find that omitting the ADC in the backwards path via a so-called straight-through estimation approximation barely impedes model learning, thus providing an efficient alternative to the classical approach of automatic gain control.