having regressed colonies using several methods, i think the best way is to use the Mann Lake PF100 series frames.
HSC takes too long to be accepted, and you really need to make it the only option for the bees...so, either you do a complete shakedown, or use a complicated method using queen excluders and trying to keep the bees from just raising a new queen outside the HSC.
Shaking down on to foundationless frames seems to bring them down to about 5.1mm....which I don't think is enough. Repeated shakedowns would probably solve this problem, but it takes a very long time.
SC foundation apparently doesn't get drawn out very well at first (I have not tried this approach myself, and rely on the observations of others). I'm also concerned about the contamination of the foundation and don't see this as enough of an improvement even if it did work well.
The Mann Lake frames (pf100 series NOT THE 500 SERIES) are 4.95mm cell size (0.002" larger than 4.9). The frames are cheap (much cheaper than HSC), they require no assembly, even if you get them coated with beeswax (which you should do unless you have your own known source of uncontaminated wax to coat them with yourself), there is so little wax present that the contamination isn't nearly as much as you can get from wax foundation. Our experience this year is that the bees take to them quite readily and draw them out perfectly. These could be fed into the middle of the broodnest a little at a time and get the regression happening at a reasonable pace...shaking a package onto this stuff is ideal, IMHO.