To make sure I understand, it sounds like you have three different MIDI files:
1. The Melodyne notes MIDI file.
2. The Melodyne tempo map MIDI file.
3. An existing MIDI file that you want to add the Melodyne MIDI notes into.
That is correct.
In the Melodyne notes MIDI file, you want to keep everything at the same positions in seconds, but change the tempo, measures, and quarter-note-based durations to musically correct values. Then you want to add the Melodyne MIDI notes into your existing MIDI file.
That is also correct.
Question: What is the resolution of all three MIDI files?
Melodyne notes: 1920 TPQN
Melodyne tempo map: Most are 1920 TPQN, one is 48?
File to add in to: 240 TPQN
The Melodyne files (in this particular case) are the 5 parts of a 5-channel sound at the very beginning of the song. It it a robotic "indistinguishable" voice that plays before a boss comes on the screen to fight. I've then merged those 5 single mid files in to a combined file using Anvil Studio, it is 1920 TPQN.
Idea 1: Use Sekaiju and temporary SMPTE resolution.
So far so good! Now to test the merge. Please hold.
Merge appears successful! This "clip" is super short, only a couple of seconds long. Hopefully it all still lines up if I have to do a longer one eventually. And I have to find a good sound in my sondfonts to use :P I have one that's decent (64 117 Lightsaber XGM from ColomboGMGS2) but hopefully I can find an even better one.
Idea 2: Use the Cakewalk "Set Measure/Beat at Now" command.
I'll pass on this one

Unless it's something I might need to try later on for a longer clip.
I wonder why Melodyne exports a separate tempo map? If it already knows the tempo I wonder why it doesn't just create one MIDI file with both the notes and the tempo value?
Jason wonders the same...
I think it's for when it is used as a plugin for certain DAWs? Not sure why the standalone version would not combine them. I can manually set the tempo within Melodyne, but it still exports the notes file at 120 bpm no matter what.
I wonder if MidiEditor is having problems with SMPTE resolution format?
It's a freeware editor, and I believe there are certain things is just does not handle properly. I rarely use it, but have it on hand to test things out sometimes, like this!
If your MIDI files have different resolutions, I wonder if that could be causing unwanted stretching when you merge in Anvil Studio.
When merging files in Anvil Studio, the first file that is open is the "main" file, and any files merged in to it take on its properties.
So trying to merge a 120 bpm file into a 62.5 bpm file keeps the timings the same, so 120 beats from the 120 bpm file still take 120 beats in the 62.5 bpm file, effectively more than doubling the playback length of the 120 bpm segment.
Changing the bpm of the original file to 120 in Anvil Studio and then merging still does not provide a correct merged file, because it does not change any of the internal timing, just the playback speed, so the 120 bpm add-on still ends up overlapping the now extra fast playing original file.