Amycolatopsis are similar to Streptomyces but their mycelia may fragment at some stage of their life cycle; and they have different profiles of production of secondary metabolites.
PCR using 16S rRNA primers. Sequenced by Sanger. Can be done in 1 day if you have the ability to do it in house (much faster than restreaking the colonies on selective media since they are slow-growing). I also wouldn't too rely on "simple tests" if distinguishing these is truly important to you. Assuming the strains you are working with are well characterized (for instance their genomes are secondary metabolites are known), a quick mass spectrum of the excreted organic-soluble metabolites can confidently and rapidly distinguish the genera.