Okay, so I'll amble in.
One of the things that I like about past tense, both third and first, is that it gives the dialogue more weight. Dialogue happens in present tense, and since I use a lot of internal dialogue (first person seems to be my default at this time), it helps to distinguish it from the narration.
So really, for every book with dialogue, written in past, it is a mixture of tenses and it's a common, accepted literary device.
I noticed in Hunger Games, which I otherwise quite like, the use of present tense blunted the effect of the dialogue.
Now, all that said, you are writing an epistolary novel, which has different conventions still. My first book was quite similar in some ways. I wrote a biography of an aunt who I truly admire for her ninetieth birthday. I self-pubbed it, because it really was meant as a gift, and I expected a small readership. (I was not disappointed in this.)
The point is, I did it all in the form of interviews. Anyone reading this work would want Ellen's thoughts, in a more documentary version, rather than having it filtered through my perceptions. I put in not a single sentence of description. It was all dialogue, edited with Ellen's input, and there was a reason for this. A good one, I flatter myself, although that is of course a matter of opinion.
Since it was a biography, it came out as a mixture of past and present, because it was a series of reminiscences, and Ellen's thoughts on the same. And it worked just fine, although it was a special case.
So my point is, what's the reason for writing this as an epistolary? And I don't mean your personal one, which can be as simple as it's a challenge that fascinates you. What is the reason your MC is telling his/her story in this form? There should be a reason, and it should be compelling and evident to the reader. As a for-instance, you could tell a story in past tense of a character who dies. That's your twist. But IMO there has to be a reason for it.
Given that there is a compelling reason, present tense is common in tweets, perhaps, but past tense is common in letters and emails. At that point I would ask, are tweets really necessary? What do they say that an email can't express just as well, or better? It would be hard to say the reverse.
One reservation I have is your comment about lack of character consistency, but that you feel it's okay because it's magical realism. (Why on earth do we have to get so obsessively categorical with fantasy?) In any novel, but especially in spec fic, you have to be consistent with your character(s). You are already asking for a major suspension of disbelief with your fairies, zombies, Hogwarts, or personally owned hovercraft. If you ask readers to forgive lapses in characterization as well, I believe it turns into 'how many impossible things can you believe before breakfast?'
And also, as a reader, lapses in character are the one thing that will cause me to hurl a book across the room and never pick it up again. Growth arcs are fine. Lapses are not.
I hope some of this helps.