Should contractions like "'til" be capitalized in a title, when in the middle of a title? What if the "'til" is the first or last word? An example of this is the album "Dog Party - 'Til You're Mine" (Spotify capitalization; the album cover has it stylized in lowercase).
There is no contraction "'til."
There is the word "until." There is also the word "till." Both of those words as prepositions have a meaning in common. "Till" is not some bastardization of the word "until." Even William Shakespeare used the word "till":
JULIET: I will not fail. 'Tis twenty year till then. I have forgot why I did call thee back. ROMEO: Let me stand here till thou remember it.
So any title where you might feel inclined to use "'til" should use the actual word "till."
That said, in response to the general basis of your question, which asks what we do with the first letter of a word when it starts with an apostrophe because part of it has been contracted out and when it either starts a sentence or appears in a title, the answer is you capitalize it. The above quote by William Shakespeare provides an example of this with the word "'tis."
Another example of this is when "'cause," meaning "because," starts a sentence.
'Cause I don't wanna fall in love.
A third example is found in the first line of the poem "A Visit from St. Nicholas":
'Twas the night before Christmas, when all thro' the house...