I've read through it, but haven't had much time to respond as of yet :)

In general, the system seems reasonably sound, though I don't think it breaks much new ground. The system is basically based on two factors: Points/Rank and Points/Stone, depending on board size. Combining them gives you a Handicap+Komi for any rank difference for that board size. The same method underlies many other such systems. I've made one such table some time ago, which can be found at HermanHiddema / Handicaps And Komi For Other Board Sizes.

There is a concern here, however, that these factors are not constants. The Xth handicap stone is not necessarily worth as much as the (X+1)th handicap stone or the (X-1)th handicap stone. Some statistics on handicap game results can be found here. The graph seem to suggest that not all handicap stones are created equal. In particular at the fifth handicap stone the winning percentage for black drops significantly, suggesting that the first four (corner) handicap stones are worth more. Perhaps the placement of the fifth stone at tengen has something to so with it, and maybe free placement would not result in the same dip in the graph. Regardless, it is an uncertainty, though experience does seem to suggest that the value of the stones is roughly equal.

I've never seen the differentiation between Chinese and Japanese style rules written out like that, primarily because most sources recommend a handicap system for the prevalent rules in their area. The distinction is certainly a valid one, as can be readily proven by the case of the 5x5 board. For 19x19, current statistics point to a correct komi of 7 for Japanese style rules, not 6. See Komi / Statistics. As far as I know, there's not much in the way of statistics from professional games on other board sizes.

First of all, this is a very interesting approach (and currently the only one), as we seem to near a universal formula for H/K calculations. If an easy solution exist is another question...

Have here are a few 2c of mine. The formulae have been lingering for a while in my HP48, but other stuff carried me away. I am still trying to remove the "if" parts in the formulae because I don't see why there should be such artificialities if everything else is just linear: players should understand what H=1 means ("=no handicap") or H=0 (="no handicap"), rather than having to introducing branchings in the formulae; also, the formulae should behave without discontinuities when using negative rating differences (the result should be just the same) - at first sight this seems to be the case.

1. a weak point of the formulae are board factor and stone value: both seem empirical and "one needs to believe" - it might very well be "manipulated constants" to make the output look acceptable.
2. I wonder if it makes mathematical sense to include the 0.5 to discard jigo: I think that an ideal formula should not take purely practical (ie tournament related issues) considerations into account, so I question the presence of this constant. The 0.5 should be a "post-computation decision" only.
3. I'm not convinced that komi starts at 6.5 for equal players for each board size; see also Wedge's input on Mathematical Bounds of Komi.
4. I'm not convinced about the linear relationship between player difference and H value. look for 'linear' on Handicap for smaller board sizes.
5. the formulae only take rating difference into account, so will result in the same output for a 30k-29k, a 4k-3k or a 6d-7d difference: shouldn't there be a compensation for the general level of both players?

Here's the next step: I think that there must exist formulae that exchange H for K: for example, if H/K calculations are well understood, a good system should be able to propose equivalent sets of (H/K) values, so handicap and komi should be interchangeable, and players should be able to choose whether to play with handicaps (and komi) or only komi (but bigger values then). That's the next mathematical challenge to solve, that IMO would prove whether this set of formulae is correct or not.

1. Edit added: and then there's the conlusion of http://www.altespace.org/go/no_handicap/, where komi might be 7.5 ?
2. Edit added: certainly see also http://www.dragongoserver.net/forum/read.php?forum=5&thread=27155 - which makes me wonder who came up first with the formulae :-)