The Grammarist has some interesting insight on this. It seems that:
Canadian English also favors practise as the verb (like the Americans), but practice appears with relative frequency as a verb (about a third as often as practise).
So your query is not totally ungrounded. Practice and practise are used as verbs in the same country, yet not always with difference in meaning. The Grammarist goes on to reveal that not even the Americans are completely innocent:
This ngram graphs the use of practiced and practised in American books published between 1800 and 2000. It suggests that the verb practise has been in decline since the 19th century and is only rarely used now.
So there you go, they are both used in the USA, too. But if you look up examples of practiced and practised in the Corpus of Historical American English, you will find that they are used interchangeably to mean train or perform but only practice seems to be used to mean to carry out a profession. I even found one example with both verbs used in the same sentence:
After the run they began practicing [performing] the commands they had practised [trained for, exercised] earlier and the stallion had reacted perfectly. Darrel decided to head back. (Fan Fic, Darrel of Pellucidar)
So in America, at least from the COHA examples, it looks like you can use either, as long as you reserve the spelling with c for the meaning of carrying out a profession. Just bear in mind that nevertheless, practise tends to be rare, and it makes me wonder if it is not used in a kind of hidden desire to "sound" British in writing. Merely in passing, the GrammarMonster notes that:
Some in the US are starting to follow the UK convention.
On the other side of the Atlantic, it is practice that is said to be rarely used as a verb, so rarely that it makes you suspect it is a typo. Hansard examples of it are scarce:
However, as someone who has practiced 781 the law for 35 years, I must make the point that ... (Mr Andrew Phillips, 2000.03.28)
(That's one of the 4 instances of practiced vs a crushing 450 of practised).
Here, however, there is proof that both terms are used in the UK, too. Instead of being a typo, it looks like practiced begins to circulate more after the year 2000 as a verb obtained through verbing from the noun practice (with meaning 3 that you provided).
Yet, it looks like this is too fresh an increase in use to be dealt with in grammar books. James D. McCawley doesn't mention anything about this in The Syntactic Phenomena of English. CaGEL is quiet too, though it uses the word profusely in its grammatical explanations, (very often as a noun with the meaning of linguistic habit). Quirk was published some 35 years ago and did not comment on it. So I am afraid that Ricky is right, it is not easy to find a reputable reference for what you are advocating.
Most sites stick to the traditional distinction between AmE and BrE and between nouns and verbs for the BrE. I suspect issues as your one here will be raised in the future, but for the time being, you can only wait for an experienced linguist with the feel of the pulse of language to stop by and share his yet unpublished knowledge.
I almost gave up looking, when I found this very interesting article which goes through the etymology, pronunciation and orthography of both noun and verb, explaining modern use of practice/pracise. The author, Tom Freeman, is an assistant editor for a charity in London, and he is in favour of the American use. He writes:
Let’s face it: this distinction is pointless. The Americans are right to reject it. It serves no purpose other than to make some people feel confused, to make others feel smug, and to waste everyone’s time. Precisely zero confusion would result if we spelt the verbs and nouns the same way. Why do we in Britain have this distinction?
After a competent analysis of the evolution of the word, he concludes:
In more recent history, the Google Books data shows that, from 1800 to 2000, the practice spelling of the noun has reigned supreme, with practise very rare. The verb’s spelling has been more mixed, but practise has consistently been well ahead of practice – until recently. This recent rise in practice as a verb might be part of the catastrophic modern decline in literacy that swivel-eyed liberals have inflicted upon our once-great education system, but I think it’s more likely that this is a sign of growing American influence.
It is of course only one opinion, but it is expressed in a decent and capable manner. The author even has a prophecy:
I think we’re in the middle of a generational shift. Soon, dictionaries will accept practice as a variant spelling of the verb. Then, as it becomes more and more popular, they’ll stop labelling it variant. Practise will survive but seem old-fashioned, like whilst or homoeopathy. Those of us who’ve had the distinctions drilled into our heads will continue to twitch when we notice a “wrong” spelling, but in time we’ll die out. The earth will close over our heads and English will live on, that bit more efficient for being rid of us.