I don't have experience with human data, but I have assembled a few fish genomes.
I know when dealing with NGS, NUMTs are a consideration, but would this be as relevant with long-reads that likely span adjacent autosomal sequences?
We didn't really consider the effects of NumtS since we were assembling the whole genome, but I think you can take that repo you linked and use their considerations to move forward. Since you're working with long reads, you could only accept reads that are x% or more mapping to known mitochondrial sequences. This has some downsides to this approach, hence a few thresholds might be good to test.
If I have whole-genome alignments alread, would it be a simple enough case of extracting reads aligned to the chrM and assembling those?
Touched on in the above statement. This could form the basis of your approach. However, by only accepting reads that already map to known sequences you may be reinforcing existing biases in that assembly. Likely not as big a problem with MtDNA, but still worth considering.
I'd also be interested in leveraging short- and long- reads to do a hybrid assembly if that produced better results.
There is a recent discussion on here about the benefit of polishing assemblies that may be useful to refer to. There's also plenty of literature on the topic.
