"believing instead that" is correct and usable in written English.
You can use it when contrasting two ideas and showing the preference for one idea over the other. For example, "John had always relied on hard work to achieve his goals, believing instead that luck had nothing to do with success."
I've taken the opposite view – believing instead that faith is a great starting point for politics.
Her colleagues were skeptical, believing instead that an indefinable combination of various genes and environment were the cause.
"It's miles over my head," he would say, obviously not believing it, believing instead that it was beneath him, who dwelt among firm, clear numbers.
"Mothers are not supposed to give guidance," she said in a 1998 interview, believing instead that children should do their own thing.
Most of the time, the investors' shared awareness of reality belongs to a Goffmanesque frame whereby they accept no intentionality, misrepresentation or fabrication, believing instead that the 'performers' (investees) are not intending to deceive them.
Some women wished for more "self-regulation", but were pessimistic about this happening, believing instead that state regulation may be necessary.
It believes, instead, that reckless behaviour might be discouraged.
We do believe, instead, that a peer-to-peer-generic solution is feasible.
Most sports sociologists, however, challenge this hypothesis and believe instead that research confirms that violence and aggression are socially learned.
Prum believes, instead, that the females have evolved to like this particular sound, a rising and falling whistle.
They believe instead that high performance people are generally self-improving through experience, observation, introspection, reading, and discussion.
