"instead being" is correct and can be used in written English.
It is usually used to contrast two similar actions. For example: "Instead of being nosy, I decided to mind my own business."
He is, instead, being held as an "enemy combatant".
It turns out he was instead being moral, even religious.
It is neither rocky nor gaseous, instead being made largely of ice.
"Otherwise, instead being a positive act, it will cause a serious problem," she said.
Waisberg added, "My children are instead being indoctrinated into a neo-Zionist theocracy".
He has not had to do that, instead being content to let the ball go elsewhere.
Instead, being grateful for small things every day is a much better way to improve wellbeing.
First, asylum applicants were barred from accessing all benefits, instead being issued with food vouchers.
That money is instead being spent on things like broadcasting football matches on BT Sport.
West Papua has largely missed the Indonesian industrial revolution, instead being compelled to finance it.
In no cases were parents given a choice over the conscription, instead being told their boys "must participate in jihad".
