The most simple and IMO reasonable solution would be to make the DoT's only breakable by direct hit from a mob. Just like it interrupts you while casting direct damage, it would only interrupt your DoT by either hitting you, or going away to more than your-casting-distance.
Some damage adjustments might be needed for that (possibly to nerf DoT further), but it would at least make some sense, and give some use to it while soloing.
This way if you put DoT on something and know the place well to not run into other agros, or social helpers, you could use it. If the mob is fast, or you have no idea if you'll run into other mobs, use direct damage. This would involve player skill (i.e. not the character skill), and would be fun to master.
Or if you have a tank keeping a mob, you could also DoT for the period (costing you sap for sure), which is also a reasonable team play between either healing, or helping to kill it quicker.
Some damage adjustments might be needed for that (possibly to nerf DoT further), but it would at least make some sense, and give some use to it while soloing.
This way if you put DoT on something and know the place well to not run into other agros, or social helpers, you could use it. If the mob is fast, or you have no idea if you'll run into other mobs, use direct damage. This would involve player skill (i.e. not the character skill), and would be fun to master.
Or if you have a tank keeping a mob, you could also DoT for the period (costing you sap for sure), which is also a reasonable team play between either healing, or helping to kill it quicker.