Didn't David consider his prayer to be sacrifice in verse 2? If not, please explain how you see something else in the text. Why don't you explain to us the real meaning because there is nothing in the other verses which would negate that conclusion?
In your earlier post, you accused me of this:
By attempting to restrict the definition of "prayer" to only what you personally dictate it to be is an example of the logical fallacy of "overly broad or narrow definitions".
I was merely pointing out that you were doing exactly what you had accused me of by your selective use of an obscure definition. I wasn't the only one who immediately spotted your cherry-picking and the obvious conclusion that the most common definitions established the link between prayer and deity and/or worship.
Please think this over again.
Since you missed the point entirely, why would I waste my time with a rebuttal of something I didn't say?
I assume you are still trying to find that Biblical example of a legitimate prayer offered to someone other than God? (I specify legitimate because I'm not interested in pagan prayers offered to Baal and other false gods.)
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In that text you cited (Psalm 141:2) David did NOT say that all prayer was sacrifice, or that all prayers must be directed to a deity, as you claimed. Let's read it again:
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"Let my prayer be set forth before thee as incense; and the lifting up of my hands as the evening sacrifice."
Psalm 141:2
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David is asking God to let his prayer be set before God as incense, and the lifting up of his (David's) hands as the evening sacrifice. What David means there is exactly what he says. No person with at least minimal competence in the English language would seriously claim that David was saying there that all prayer by every person at all times was a sacrifice, or that all prayer must be directed toward a deity, any more than they would claim that all prayer must be accompanied by the raising of ones hands.
Then you issued this challenge: "I assume you are still trying to find that Biblical example of a legitimate prayer offered to someone other than God? (I specify legitimate because I'm not interested in pagan prayers offered to Baal and other false gods.)".
For one quick example, let's turn once again (like you did) to David:
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"Bless the Lord, ye his angels, that excel in strength, that do his commandments, hearkening unto the voice of his word. Bless ye the Lord, all ye his hosts; ye ministers of his, that do his pleasure."
Psalm 103:20-21
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In his prayer recorded there in Psalm 103, David is talking directly to God's angels, exhorting them to "bless the Lord". His prayer at that point is specifically directed to angels, fellow created beings.
To help you learn more about these matters, and for some more biblical examples of non-worshipping prayers to other created beings, here are a couple helpful links: