Eugene Volokh, a known grammatical relativist, scoffs at “to increase dramatically,” as if “to dramatically increase” would be better. But better in what way: clearer or less stuffy? The meaning of “to increase dramatically” is clear. The only reason to write “to dramatically increase” would be to avoid the appearance of stuffiness.
Seeming unstuffy (i.e., without standards) is neither a necessary nor sufficient reason to split an infinitive. The rule about unsplit infinitives, like most other grammatical rules, serves the valid and useful purpose of preventing English from sliding yet further down the slippery slope of incomprehensibility than it has slid already. If an unsplit infinitive makes a clause or sentence seem awkward, the clause or sentence should be rewritten to avoid the awkwardness. Better that than make an exception that leads to further exceptions — and thence to babel.