For your My Tasks, what works for most of us includes some automated rules + some manual triage. Many have followed my prescription, which offer flexible options including time blocking, in case that’s what you describe. Just follow the steps and suggestions here:
For your contractors not using Asana, consider two solutions (they’re quite different approaches). The first is using Asana, the second uses Asana2Go (Disclaimer: I’m the creator) which addresses the situation where you are in Asana but you work with folks who are not.
Hope one or more of these three things help; maybe all of them!