I have checked the DESeq2 normalizaion result, the sum are also different between samples like FPKM/RPKM/TPM. In your idea, i think use RPGC(1x average coverage) are better.
In most paper(about cancer) when show the gene change quote from TCGA adopt the FPKM instead of DESeq2 normalization result( TCGA produce the raw count)