I coughed more when dual using than when vaping, it seemed to me (to be) the fact that I was asking my lungs to handle two different "things" at once, and it did cause more coughing. With that said, a 0.6 coil is sub0hm and it certainly could be the density of the vapor, or too much nicotine for that perticular coil. I started out sub0hming and I hated it. Even lowering my nicotine, I do better with higher resistance coils, in a MTL vape.
For setups a bit more adjustable and customizable than the breeze, I would maybe recommend a pico mod, although depending on which model, you may not want to get the Melo III tank kit, that is also a slightly sub0hm vape, but you could put another MTL topper on there, like the Nautilus 2, the nautiilus mini and etc. Those coils have a much higher resistance (although you can get a 0.7 coil down the line, if you want more vapor. Or you could consider an aspire zelos kit that comes with the Nautilus 2 coil. You would then have the ability to alter coil type, wattage level, and airflow, helping you dial in a vape that suits you. Or, you could go for a small, AIO kit, although again, some are moe customizable than others. But generally I'd say perhaps look at small, MTL kits (whether a small box mod, or something more tubular) might be a good plan. You may need higher nic level to get satisfaction, but I found myself coughing much less and able to vape more, which got me away from dual using more quickly.
With that said, a certain amount of coughing when switching is normal. It will happen if you dual use, but also during detox. Detox MAY start while still dual using, although I don't tend to see that so much. So, even if you get the "perfect vape" you may cough along the way. With that said, if you are coughing so much you can't really get to vaping regularly, that is a problem, so I agree with you idea of looking at other setups, and the Aspire breeze may WORK for you down the line, once you've fully transitioned. I can handle more volume of vapor the longer I vape, although I'm doubtful that I will ever become a dedicated, really low sub0hm vaper.
Best of luck and welcome. I hope you find success and I'm sure you'l get many other ideas on gear from others...
Anna