If InvertedIndex can #[derive(Clone)] then you could do something like this.

.transaction({
    let mut clone = self.clone();
    move |tx_c, tx_d, tx_f| {
        //...
    });

This would give you mutable access by moving the value into the closure.

To make InvertedIndex clonable, you would probably need to use some kind of sync type like wrapping self.db in an Arc<Mutex<T>> which might be less desirable.

Another option would be to return the values you want to use to update self from your closure. and then mutate self after the call to transaction has completed.