I don't think praying goes with practice of japa and meditation. If you can't get over praying, do that after your meditation, puja etc as is the common practice.
Kapila in Mahabharata, Shanti Parva: Those who perform sacrifices and other rituals without expecting anything, just because it is Dharma to perform them, are freed from all passions, egoism and sins, obtain certain knowledge and hold fast to it, and work for the good of all beings. They are always content, happy, peaceful, sincere and honest, and conduct themselves according to the Vedas.
One cannot pray without expecting something, so I think it is not the best form of worship.
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