I ran a Google Books search for four words that could arguably mean "the state of being dynamic"—dynamicality (no line), dynamicism (blue line), dynamicness (red line), and dynamicity (green line)—with the following results:
The line for dynamicality is "no line" because the Ngram search returned too few results for that word to permit mapping it. A Google Books search turns up 12 matches for dynamicality, dating back to 1913. Given that the OP views dynamism and dynamics as unsuitable to use because of other connotations that those words have, it seems reasonable to consider brifly the connotations of dynamicality, as suggested by the first two Google Books search results that include the word.
From William Quayle, "Christ's Resurrection, the Core of the Gospel," in The Christian Advocate (March 20, 1913):
A sinless Christ answers for a resurrection; and a resurrection answers for a sinless Christ. In Jesus rising from the dead is no thing incompatible with wise thought. Who was Death to throttle Him? That is how we see it and how we feel it. The Man Christ Jesus rose from the dead. Here is the masterful proposition and the complete dynamicality. That Jesus ascended through the springtime sky and walked in quiet on the unquiet sea and, having compassion on a multitude. invited them to take supper with Him, are trivial exploits to Him who surrendered Him to the depths of death and on the third day could not be holden of the grave. O phrase of eternity, I hear thy holy bugles blowing transcendent triumph. God-Man has proven king over death.
And from Leo Wertheim, Solution of the World Riddle, volume 1 (1931) [combined snippets]:
Now, the universe is only name-verbally existent and only name-verbally active, dynamic. We learn more definitely farther on that it is made up of only object-Names as things-themselves on the one hand, and what those Names but verbally do, on the other hand. Thus it is a whole made up of Names persisting as Ultimate Being, and what Being does as the verbal process which it is. Verbs themselves constitute the essential dynamicality of universal Being. The world naturally has this name-verbal dynamical structure a priori; that is, everything is "given," everything is "intuitively" what it is and what it does. Because a dream is of course all "Intuition." There is no one in the dream who makes any distinctions. The distinction between the "given" and the "inferred" disappears. In a dream everything is only once, and that one-time-being is a priori. Accordingly, the universe is Cognition itself.
More-recent matches dispense with the spiritual/philosophical trappings of the earliest usage and treat dynamicality as neutrally as other sources do dynamicness, dynamicism, and dynamicity. Still, it seems fair to ask what (if anything) makes the relatively rare form dynamicality preferable to the more widely used forms dynamicism (36 matches for the period 2005–2008 alone), dynamicness (23 matches for the period 1980–1994 and roughly a hundred matches between 1914 and 2010), and dynamicity (48 matches for the period 2007–2008). Does English need all four terms? To say nothing of dynamicization (roughly 90 Google Books matches) and dynamization (hundreds of Google Books matches)?
The trouble with blithely coining neologisms is that, when lots of people do it, you end up with a parking lot full of loose change to wade through—with no dictionary to help you figure out what distinction (if any) the coiner intended to make with his or her preferred term.
If you can't bear to use dynamism, I recommend using the most common of the recently propagated competing alternatives, which the Ngram chart above suggests is dynamicity. Because no one wins when readers (and writers) have to pick and choose and guess their way through four or five or six unfamiliar ways of expressing the notion of "the state of being dynamic."