I think you're right Steve, it is dependent on the highlights. In circumstances where the highlights are muted or non existent the Helios performs pretty much as any other lens of its type. This is wide open with a 44M and the background is between 1 and 2 meters away.
I've quickly looked through hundreds of Helios 44M and 44-2 pictures and I can't find any swirly bokeh pic's. Most of my stuff is close / detail pictures shot wide - usually a stop or two down at most - and that's where I would expect the swirls.
This is about the best I can find for wide open and backlit, but there's an ND4 filter chopping the light down.
And I don't think that shows big swirls, there's a bit in the water reflection but that's very little and might not actually be the swirly attribute of the lens ? I think it is strong and small pinpoints of back light at certain apertures that cause it, I don't think it's an automatic feature of the lens.
I'm not sure what the design of the Chinon is compared to the Helios, but the swirls from that lens is hard to get away from. I actually dislike the swirly bokeh, but I use both the Helios types a great deal on various cameras from K10, NEX to an assortment of film bodies. Perhaps we have different light over here?