I think this is a reasonable idea.
However I think it's wonderful that lesswrong has a norm of offering monetary bounties for work. This is a norm we should encourage, and I'm worried introducing non-monetary bounties will make monetary bounties less common.
StackOverflow's bounties seem pretty similar to what you describe. They also seem at least somewhat successful.
I like the idea. My intuition says that 1:1 transfers are best to get closer to a monetary system. The ring up voting is a problem because it creates value out if nothing. I think I would distinguish between karma that is spend on upvotes and Karma that is transferred. The idea being that you can not spend karma that was used to upvote. Maybe the default could be that half goes to the upvote and half to the account - but maybe you can split up differently. This would recover your 1:2 effect.
I fear that making karma more like a currency is not good for the culture on LW.
I think money would be preferable to karma bounties in most situations. An alternative for bounties could be a transfer of Mana on Manifold: Mana is already (kind of) a currency.
On LessWrong, we can weak- and strong-upvote posts, which adds to the other user's karma without impacting our own. As we gain karma, we are able to award more karma. I have nearly 10,000 LessWrong Karma, and my strong upvote awards 8 karma at no cost to me.
Many users offer monetary bounties or after-the-fact money awards for posts or comments that they find especially useful. These contests are often fun, motivating, and a costly signal of genuine appreciation. Over $500 in prize money has accumulated for fact-checking Jake Cannell's Brain Efficiency, and I offered a $10 micro-bounty for answers to Vanessa Kosoy's questions about technologies stuck on initial adoption.
I think the benefits of a bounty or award offering extend come from the structure of the reward rather than the fact that it is offered with cash. And so I think we could achieve a similar bounty/award-like result if it were possible for LessWrong users to directly transfer some of their LessWrong karma to other users.
For example, if I liked your response to my question, what if I could transfer 50 karma points from me (-50) to your comment or post (+50)?
Benefits
Refinements
We could make it cost 2 karma to transfer 1 karma to increase the costliness of the signal.
We could let users spend karma to downvote other users more heavily to prevent an asymmetrical situation where controversial posts blow up to 2,000 karma because their detractors can't downvote as heavily as proponents can upvote.
We could set a maximum cap on karma transfers for a single user and post/comment if things were getting out of hand.
Potential objections and responses
Objection: Why wouldn't people just go through another user's posts and systematically upvote them if they wanted to give a large karma award?
Response: First, this behavior is possible to moderate away. Second, it doesn't endow a specific post or comment with a large award. I anticipate that users who wish to recognize a particular comment or post will want to attach their award to that specific post or comment, and that they'll be willing to "pay a premium" in order to do so.
Objection: What if this was used to transfer karma from a rate-limited or banned account to a sock puppet?
Response: We could stipulate that only non-limited accounts are permitted to offer karma bounties. Another option is to "charge" 2 karma for every 1 karma transferred, such that a 50 karma award costs 100 karma, meaning the sock puppet would only have half as much karma as the original account. It would also be a pain to do this in a low-visilibity way, and again, it would be easy for mods to notice when rate-limited user A is giving huge karma awards to brand-new user B for apparently no reason.
Objection: Doesn't this tend to limit our ability to get rid of bad posts by downvoting them, since a small but passionate minority could force them into prominence?
Response: First, it might be good for LessWrong epistemics to enable this sort of costly signaling by minority groups. This is especially true if karma transfers cost more to give than the receiver earned (i.e. spend 2 karma to transfer 1), which would limit the ability of small groups of like-minded commenters from ring-upvoting each others' unpopular opinions without end. Second, I call this "karma transfers" because I'm actually open to the idea of being able to spend your own karma to more heavily downvote posts you think are particularly bad.
Objection: Wouldn't people hand out giant upvotes or downvotes like candy, leading to a very different structure of visibility of posts than we are used to?
Response: Possibly, although that might not be a bad thing. We could experiment with this feature for a month or two and see if it did good things overall for the site. Alternatively, users could opt-in or opt-out (perhaps only allowing switches once per week or something, to avoid users shielding themselves from impending karma-transfer downvotes). But also, I have 10,000 karma accumulated over several years, meaning that if I awarded 50 karma on a spend-1-to-give-1 basis, I could only hand out 50 karma to a total of 200 posts/comments before I was equivalent to a new user. On a spend-2-to-give-1, I can only hand out 50 karma 100 times.