This post is a rumination of sorts, without an answer. If you come here for clarity then step away from the screen and take tea!
Some geezer in whose company I sat last week did that thing which mildly irritates me (and Giles Fraser too, apparently) and went down the Cheesus route in prayer. "Dear Cheesus ..." and lots of Fr God too (I must have missed God's ordination). I pondered, I did, and quite a lot.
I wonder what it is that determines upon which person of the Trinity we place our Post-It Note prayers? It is manifestly the case that conventions exist along broadly the same lines as variations in ecclesial expression. Some people will always kick off a prayer in the "Almighty God..." mode, while others ordain God. Others will talk to Jesus and others will appeal to the Holy Spirit. Some take the more intimate birthday card route, "Dear God ..." or "Dear Jesus..." and others, perhaps bored with the same old same old will do something creative with "God of our healing/creation/salvation ..." stuff. Beyond that, you get the valent approaches that apply an adjective to the deity in the frame, "Loving God ...", "Mighty Spirit ..." and all that.
This caused me to chew on the proverbial wasp in my darkest inner-monologue too. I might be burned as a heretic for this, but there is something deep down that is irritated by prayers directed at Jesus specifically, a historical figure, himself quite infamously made dead by Romans. Prayers to Christ I can live with, but the voice in my darkest dark place keep yelping "But Jesus isn't alive" when that schema of prayer is applied. It goes to my modest suspicion of those who proclaim a personal and intimate relationship with Jesus as distinct from God or Other. Perhaps it just betrays my suspicion of public intimacy at any level and judges me as the cold-hard misanthrope that I have probably become. Sadly, this comes to play for me when the greatest linguistic travesty is enacted - in applying the benign term "lovely" to God or any part thereof. "Lovely" is for kittens and Bambi, not for a God who, through his treatment of his Son, would surely fail to secure a clean CRB disclosure (and would thereby be prohibited from running a youth club or a parish).
I arrive at no conclusions with this stuff, as much as note down what is going on within the dungeons of my heart. But please don't despair if you are a "Dear Jesus ..." type of praying person; you are lovely too.