I would say that one of the skills that complements reading, is knowing when you need to read and when you don’t. This is something that comes with experience. There are plenty of situations on the board when you know the expected outcome of an exchange. Joseki is just one example of that. When you see something unexpected, that is a signal to slow down and carefully read it through.
You get better at reading by practicing reading. For me, most reading mistakes in a game come from
Not reading at all: not checking whether a group is alive, not checking whether two stones can be disconnected, playing a shape move automatically, not checking whether a stone can be captured in a ladder or in a net, playing joseki automatically ignoring the context.
Considering only one move
Considering only one response from the opponent
Chickening out: add an unnecessary defensive move or play a less ambitious but safer move.
Stopping one move short. The solution was one move deeper.
Reading under time pressure is hard. For better reading practice,
Play games with long time settings, and use your time.
When you are in byo-yomi, your reading can’t be as accurate, but do continue to read, and try to read faster (yes that sounds silly but obviously we play worse with 30% brain capacity than with 80% brain capacity).