Playtesting has been informative. I'm happy to say that the proposed hand and deck arrangements provide for much livelier play.
I've also been experimenting with different scoring schemes; that's where the remaining work lies. One quality that I failed to fully appreciate was the simplicity of the original system—not just in terms of the arithmetic needed to sum up one's score (everything being 10, 50, 150, 250, etc.) but also in the mnemonic elegance of how the scores are represented by captured cards.
In the original system there are really only three scoring tokens, that is, captured cards used to keep score and add up at the end of the game: face-up cards are worth ten points, face-down cards are worth 100 points, and 10♦ and Jacks are worth fifty points. Every scoring unit—100 for a glove, 200 for a sock, 150 for a glove of Jacks, etc.—can be composed of those three items.
Whatever the relative fairness or proportionality of those specific amounts, the value of a system which only has three tokens to mix and match can't be overstated. In our playtesting, the adjusted-scoring games (notwithstanding whatever degree they need further adjustment, for reasons stated above) weren't nearly as fun or smooth as the ones with the classic scoring simply because they required so much more effort and bother.
It's clear, if I do want to adjust the scores for fairness, that a similar system—three scoring tokens at max—will have to stay.