I tried the carabiner idea by just clipping my hook to a carabiner that captured the sheet lines.
Two things that I think the hook method does a little better.
First, the carabiner would end up over a foot from the clew of the sail. The point I could control and position was the carabiner itself instead of the actual clew of the sail. Using the hook where both the barber hauler and the sheet are independently connected right at the clew allows positioning the clew at a wider range compared to the carabiner. You can see this in the attached pictures. The last picture shows the hook and you can see that the sheet can still position the clew fore and aft and the carabiner is more limited. Does this matter much.. dont know.
Second, the carabiner goes around the two lines of the sheet. Even through the carabiner position may not change much with respect to the clew, the two sheet lines (for the 2:1 leverage) do move in opposite directions inside the carabiner so both are rubbing on the carabiner as the sheet line is pulled in. Plus the carabiner forces these two lines that are moving in opposite directions together further adding friction. So using the carabiner adds a fair amount of friction to the actual sheet attached to the clew when the barber hauler is tightened. The hook adds no friction at all to the sheet line and for the same tensions, the sheet is way easier to pull.
However as noted earlier, with the carabiner, your barber hauler lines dont move with your clew as you furl as noted. FYI, I just release both barber hauler cleats to furl, and that is pretty much the only action I take.
So.. tradeoffs like anything else and I liked the hook method in that link a little better.
First two pictures (hosted on FB so they will go away after a while) are the carabiner experiment (only done in the driveway and not on the water). The third picture shows the hook that is in the link a few posts back.