It might be more straightforward if, instead of coding your DV as hits and false alarms, you let your DV be a binary factor (0 or 1) indicating the participants’ responses (response_level), and let that be predicted with the true_level (0 or 1) which interacts with your predictors X of interest. So
response_level ~ true_level * (X1 + X2 + X3 + ...)
Then you have a simple Bernoulli family model. The effects of the X1, X2, ... show how the “bias” – the tendency to respond 1 regardless of the true value – is influenced by X1, X2, ...; the effect of, for example, true_level:X1 shows how the “discriminability” of the true value is changed by X1. If the link function is probit, the results can be phrased in terms of z-scores/d-prime, which might be useful. Relevant material can be found at https://vuorre.netlify.app/post/2017/10/09/bayesian-estimation-of-signal-detection-theory-models-part-1/ and https://psyarxiv.com/5ue9a/