Do these "ozone-depleting substances" also have infrared-absorbing greenhouse impact unrelated to their ozone-depleting chemistry, or is the story more complex?
Yes, the paper (I have access) actually said that the warming is because of the strong direct radiative forcing of the ozone-depleting agent rather than because of their ability to destroy ozone. They conclude this from findings of running a full (according to historical data) vs. fixed ozone-depletant + stratospheric ozone level (at 1955) vs. fixed ozone-depletant only ensemble simulations.
The paper specifically gives two examples:
Chlorofluorocarbons CFC-11 and CFC-12 are 19,000- and 23,000-fold more radiatively efficient, respectively, than CO2 (in terms of Wm^–2 per parts per
billion), resulting in 20-year global warming potentials 7,000- and
11,000-fold larger. So yes, these gases are crazy considering how much we put them into the atmosphere during 1955 - 2005
Why the different fractions; 1/3 of all global warming but 1/2 of arctic sea ice loss?
First thing is you have to know this is just what the model (based on its mechanistic representation) tells you about the relative contributions. The paper tried to explain that ozone-depletant has a higher "warming efficacy" (than CO2, CH4 & N2O) meaning that for the same amount of radiative forcing, it can produce larger temperature differences. So, this discrepancy results from the divergence of radiative forcing and actual temperature impact at a certain location. In particular, the paper said ozone-depletant reinforces the lapse-rate positive feedback and attenuates the negative net cloud feedback in the Arctic. As to how it actually works (and why it doesn't work for CO2, CH4, N2O), I am not an expert in this regard so you would have to look at it yourself. I am guessing this has to do with their molecular weight affecting their movement in the atmosphere (height where they are found relative to the vertical temperature profile and height of clouds at a particular location).
(PS. I also have a feeling that part of it may be just an artifact from parameterization to match Arctic Amplification, meaning that it is more "sensible" to adjust large warming potential gas by a small percentage than to adjust a low warming potential gas by a large percentage. But don't take it too seriously, I am not an expert in this regard.)