Honestly I would support only allowing Show HN for accounts that can downvote. It's really not such a high threshold.

It would filter out some people who lurk but still have interesting things to contribute, but despite the drawbacks that threshold is probably the most immediately impactful solution. Of course, it strongly incentivizes the purchase/selling of accounts, and karma farming, but that problem is perhaps less of a problem than all high-effort human content getting completely drowned out. There are already a plethora of spambots making comments getting upvoted, so it's not like that problem doesn't already exist either.

I'm not sure that incentive is so strong. Is it really that desirable to pay money to be able to showcase a free project?

We would have to prepare for a deluge of accounts posting\commenting just for the sake of accumulating karma to be able to downvote.

That's the key thing to remember here, that any ideas that are implemented will be suspect to gaming just to get around what ever is chosen.