First instinct is "wtp 1♥" but putting some pressure may be better.
Not one of my partners would except hand that good for 3♥, even vulnerable.
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since in SAYC PD will expect me to have more.
More of what ? You have more playing strength than standard 12 count with 6♥.
If you mean "more points" I don't see any point in worrying about this unless you play with someone who likes to double "because you opened and I have 8hcp partner" but then it's a problem with your partner not with opening...

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