How baraminology produces observed diversity

Creationists hold that baraminology explains the diversity of life observed today despite the extinction level event of the alleged global flood. This requires new species to diverge — by whatever means — from the original "kinds" taken on board Noah's ark. Todd Charles Wood estimates, from the fossil record and Biblical text, that 15 million species arose in only three to four centuries after the flood, and many of those are now extinct.

This poses a sizable problem, because proponents of baraminology are the same people who reject most of evolution, asserting that new species do not, an d cannot, form over time. According to them, only "microevolution" occurs, since horses are still horses and haven't evolved into anything startlingly different in the last few hundred years. (Creationists also have yet to clearly distinguish the "microevolution" process they accept from the "macroevolution" processes they reject, which they define as one kind descending from another.)
And there is the little issue of the separation of living things into species. If baramins are the things that were created by God, are species just accidents, things that came about by random chance after the Flood? The Bible doesn't tell us that God had anything to do with the origins of species, does it?

Extreme rates of differentiation

The problem is that evolution just does not happen as fast as would be needed. Baraminology requires a mechanism that causes diversification at super-evolutionary speeds. If genetic differentiation could occur fast enough for several thousand creatures to result in the many tens of thousands of vertebrate species alone, then it would be simple enough to submit the "proof" of evolution that creationists often ask for — showing one species developing into a totally divergent one in a few generations.
The greatly increased mutation rate that baraminology requires to achieve this differentiation would have caused severe problems in the organismal populations. The mutation rate required for such rapid genetic change would not leave enough viable genomes for negative mutations to be selected out of the gene pool.
There are an estimated four harmful mutations per zygote (embryo) Link: http://www.cell.com/ajhg/fulltext/S0002-9297%2807%2962663-9.
Normally, this is not a problem because nearly all mutations are recessive, and natural selection can weed out these malignant changes. Baraminology would require the rate of mutation to be sped up by a factor of up to 250,000, and we could expect to see a gigantic influx of mutations approaching one million detrimental genetic changes per fertilization
https://www.youtube.com/watch?v=5mPPnN1c0jk. This would result, of course, in the sudden termination of all life on earth.
In addition, genetic mutations cause most types of cancer; an increase of even a few hundred times, far less than baraminology demands, would have tremendous and fatal consequences for animal life.
Of course, one could resort to special pleading that God "switched on", and then "switched off", the high-speed differentiation. Baraminologists have presented no evidence as to why God is unwilling and/or unable to repeat such a process now or in the future, or indeed any evidence that such a thing has happened in the past, particularly as fossil evidence only indicates a smooth and relatively slow evolutionary process. Even the best evidence for rapid evolutionary change (known as punctuated equilibrium) — such as the Lenski experiment or the Cambrian explosion — do not show evolution happening anywhere near fast enough for such rapid genetic differentiation to be realistic.