Note that hg19 mtDNA is not the rCRS. This one was already present in GRCh37, which is one of the differences between hg19 and GRCh37, and is now in hg38.
Fish out Ensembl ID's of the genes from each file awk -F "\"" '$1 ~ /chrM/ && $3 ~ /gene/ {print $2}' gencode.v37lift37.annotation.gtf (this is hg19 example)
For Method 1 you could directly download the transcriptome fasta files from Gencode and pull the cDNA/spliced sequences from there (if this is what you want rather than the entire genomic gene sequence incl introns).
Note that hg19 mtDNA is not the rCRS. This one was already present in GRCh37, which is one of the differences between hg19 and GRCh37, and is now in hg38.