According to this study, the distribution is as follows:
1st declension 21.6%
2nd declension 23.7%
3rd declension 52.6%
4th declension 1.4%
5th declension 0.7%
("Development of Gender Classifications: Modeling the Historical Change from Latin to French," by Maria Polinsky and Ezra Van Everbroeck Language Vol. 79, No. 2, Jun., 2003, Table 2, pg. 362)
I suggest contacting the folks at various organs and organizations. Jason Pedicone at Paideia, somebody at the Vivarium Novum, Terence Tunberg, Nancy Llewellyn, the ALF, Reginald Foster, Gaius Licoppe, Roberto Carfagni, etc. I'm not sure any of them will be able to give you bounds on either side, but I'd bet that all of them together might give you a decent ...
Difficult to verify this research but, according to this Reddit thread, the distribution over An Elementary Latin Dictionary (Lewis) would be:
1st declension 19.14% (1248)
2nd declension 31.28% (2039)
3rd declension 45.93% (2994)
4th declension 3.59% (234)
5th declension 0.06% (4)
I'm OK with 'accuracy' as you see its etymology described in your question, but no amount of care will get the correct result if the method of getting it is biased. Accuracy and precision are almost, but not quite complementary. You can obtain a result, whether accurate or not, with great reproducibility, but you do need a word to distinguish the two and '...
I was taught Latin prose composition in a way that is now almost forgotten. There were many tricks of the trade to be acquired, including such basic rules as correctly sequencing tenses; most of these could be found in the primers and study guides — as they can be still — and one of these was how to change emphasis by altering word order, which apparently ...