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You can do this, with one exception to what you have proposed.
When a neutral is shared, the two hot wires must be on a double pole breaker.
Since it is #10 wire, the breaker is likely rated at 30 amps. But if you are planning to use the two new circuits for lighting and/or convenience outlets, I would downsize the breaker to a 20 amp.
Thanks for your help-this makes sense to me