The increasing use of wireless sensor networks and remote sensing permits real-time access to environmental observations. Data assimilation frameworks tap into such data streams to autonomously update and gradually improve numerical models. In hydrogeology, such methods are relevant in areas of long-term interest in water quality and quantity, for example, in drinking water production. Unfortunately, accurate hydrogeological predictions often demand a degree of geological realism, which is difficult to reconcile with the operational limitations of many data assimilation frameworks. Alluvial aquifers, for example, are sometimes characterized by paleo-channels of unknown extent and properties, which may act as preferential flow paths. Gradually optimizing such fields in real-time or quasi-real-time settings is a formidable task. Besides subsurface properties, ill-specified model forcings are a further source of predictive bias, which an optimizer could learn to compensate. In this study, we explore the use of a quasi-online optimizer based on the iterative batch importance sampling framework for a groundwater model of a field site near Valdobbiadene, Italy. This site is characterized by the presence of paleo-channels and heavily exploited for drinking water production and irrigation. We use Markov chain Monte Carlo steps to explore new parameterizations while maintaining consistency between states and parameters as well as conformance to a multipoint statistics training image. We also optimize a preprocessor designed to compensate for potential bias in the model forcing. We achieve promising and geologically consistent quasi-real-time optimization, albeit at the loss of parameter uncertainty.