I really like the idea of bootstrapping other experiments off the bitcoin endowments.

I'd first considered endowment reuse in the context of a crypto-catastrophe (restarting a new currency, using an old checkpoint of endowments) or coin-civil-war (irreconcilable differences which lead to two long-lived incompatible chains, descending from some common parent). But of course the technique doesn't need to be limited to such crises; it can help other experiments bootstrap with a broad audience of proven cryptocurrency adepts.

Obviously the idea is generalizable to making a distribution that's any scaling, truncation (in time or values), partial-randomization, or other function of Bitcoin endowments, as others have mentioned.

However, I think there's another supercharged variant that's possible, that I haven't seen mentioned yet. It'll seem wacky at first, but give it some thought... it may help cement the spincoin into a certain beneficial relationship with the 'seed coin' (usually Bitcoin).  

The variant:

Rather than picking a magic checkpoint, at which the spincoin distribution (for a single genesis moment) copies the parent seedcoin, issue the spincoin as a continuing, perpetual dividend from seedcoin holdings across all time, including the past, and the future (as it arrives).  

As an example, let's call our theoretical spincoin Sumcoin, and the seedcoin Bitcoin.

Imagine that for every block-tick you've held bitcoin-satoshis, you would be entitled to an equal number of base sumcoin-units. You'd redeem them with a specific claim(bitcoin-txo, start-block, end-block) action in the spincoin chain. Did your key(s) control a 10,000 satoshi output for exactly 200 blocks? Sign your spinclaim for that holding period, get 2,000,000 sumcoin-units. (Of course, that same range of holdings can only be spinclaimed once.)

That is, the Sumcoin endowments are the integral of the mother-Bitcoin holdings. If you held Bitcoin in the past but sold it all, you can still claim some Sumcoin (as long as you've retained your keys). That is, the incentivized audience for Sumcoin is everyone who's ever held Bitcoin. And, as long as you continue to hold Bitcoin, you get a stream of Sumcoin, claimable on demand.

Of course, there's far more Sumcoin numerically, and indeed its total issuance is growing by the size of the total Bitcoin endowment every block. But that's all just a giant factor larger than Bitcoin, and completely constant/predictable in both its magnitude and to which actors it accrues.

Once all Bitcoin is issued, Sumcoin's inflation is similar to Dogecoin, a small constant amount each period. That is, unlike inflating fiat monies, it doesn't use unpredictability, or closeness to the monetary-authority, to achieve surprise redistribution.

If there is a benefit to a permanently-but-predictably inflating currency, as many have conjectured, Sumcoin might best capture that benefit in a manner complementary to Bitcoin – because it's a linked funhouse-mirror-twin of Bitcoin. (That is, it might fill this niche better than coins with demurriage or other forms of permanent inflation, and other arbitrary initial distributions.)

In the large, the relationship could fortify Bitcoin's role as the permanent, undilutable equity shares of the cryptoeconomy, with frothy Sumcoin used for lower-value/higher-velocity consumptive transactions.