While driving, I heard both songs play sequentially on the radio and I realized they're both in the same key. There's a bit of tempo difference, "Hello" is slower at about 79 bpm while "Closer" is substantially faster at 95. Since stretch/compress algorithms typically sound better when you speed up instead of slow down, I decided to base the mix around "Closer's" tempo.
There is no released studio acapella of "Hello," so I had to settle for the filtered version, which works, but it leaves some audio artifacts behind (if you notice the vocals sound a bit washed out or warbly, that's why), but overall I like these two songs together. If I ever end up getting my hands on the official "Hello" acapella I'll make sure to update this mix.