I had a similar intent for less important accounts (I would keep using a more secure but less convenient solution for more significant credentials). To shortcut guessing the index you could store just the site plus index in a cookie or similar - if that data is lost you can still use the guesswork option. If tracking is a concern so you don't want site names to be stored, has the site name and index and use that to build a bloom filter (not perfect, but it will usually guess right without storing the actual data). Though for my use I wouldn't care that the site names were known.
Another similar idea to stop people using the "just add a character or increment a number" method for dealing with passwords that need to be changed monthly. The password is based upon a hash of master+site+year+month+salt. You are still compromised if the master password is compromised, it is never any worse than what people do already. Again I'd not use this sort of thing for truly important accounts.
> Kinda amazed that two people independently arrived at such a similar idea. :)
I've seen many similar schemes, some identical to those I've considered and either dismissed of not found time to think through, some with minor variations. I think this is a problem a lot of people encounter so it is a common though-game, so I'm not surprised that for every combination of tricks there are a number of people who have thought the same (or even got around to implementing something).