Is the date alphabetical? Write a function or program that accepts a date (as a string in YYYY-MM-DD format) as input and returns a truthy value if that date is "alphabetical," and a falsey value if it isn't. 

An alphabetical date is a date whose month, day and year are in alphabetical order when expressed as a string (and when considered specifically in M - D - Y order). For example, Sept. 26 2018 is an alphabetical date:

September 26th 2018 -&gt; September twenty-sixth two thousand eighteen

September
Twenty-sixth
Two thousand eighteen


Another way to think of this challenge: "are the elements of a given date lexically sorted?"

Notes:


2018 is represented as "two thousand eighteen," not "twenty eighteen" or "two zero one eight." For another example, the year 1456 would be represented as "one thousand four hundred fifty-six," not "fourteen fifty-six."
26th is represented as "twenty-sixth," not "twenty-six."
Each element of the date is considered as a whole. This is why 2018 doesn't automatically fail even though the "e" in eighteen comes before the "t" in two.


The following dates are not alphabetical:


September 2nd 2018 ("second" should sort ahead of "September")
April 30th 4000 ("four thousand" should sort ahead of "thirtieth")


Additional Rules:


You will receive the date as a string, formatted like YYYY-MM-DD. The year will always have four digits, and the month and day will always have two digits each. Zero-padding is not represented in the string conversion (e.g., '2000-01-01' is 'January first two thousand' as you'd expect).
You may assume that dates will always be valid (no February 30th, no Smarch 1st) and that the value of the year will be positive (no dates B.C.), but the date may be far in the future ("in the year two nine thousand...").
You should return a truthy or falsey value, not necessarily a boolean True or False. If you do this in Javascript and want to return '0' and 0 that's fine. Of course, if you want to return a boolean, feel free.
Standard loopholes are forbidden.
This is code-golf 


More Examples of Alphabetical Dates


2066-01-02 (January second, two thousand sixty-six)
1000-04-08 (April eighth, one thousand)
6000-08-01 (August first, six thousand)


More Examples of Non-Alphabetical Dates


1066-01-02 (January second, one thousand sixty-six)
1000-04-07 (April seventh, one thousand)
8000-08-01 (August first, eight thousand)
JavaScript (ES6), 101 bytes
Saved 4 bytes thanks to @Shaggy
Returns \$0\$ or \$1\$.
s=&gt;'_414044406550'[[,m,d]=s.split`-`,+m]&lt;(d=`_268328715819832871${6e12-12}`[+d])&amp;d&lt;'_6A9338704'[s[0]]

Try it online!
or Test all dates!
(includes some invalid inputs)
How?
Each month, each day and each year is mapped to an ID in \$[0..10]\$ (\$M\$, \$D\$ and \$Y\$ respectively) according to the following table. We then test if we have \$M&lt;D\$ and \$D&lt;Y\$.
The last part of the lookup string for day IDs is slightly compressed by using ${6e12-12}, which expands to 5999999999988 (19th to 31st).
  M | Month                D | Day                  Y | Year (millennium)
----+----------------    ----+----------------    ----+-------------------
  0 | April                1 | eighth               0 | eight thousand
  0 | August               1 | eleventh           ----+-------------------
  0 | December             1 | eighteenth           3 | four thousand
----+----------------    ----+----------------      3 | five thousand
  1 | February             2 | first              ----+-------------------
----+----------------      2 | fifth                4 | nine thousand
  4 | January              2 | fifteenth          ----+-------------------
  4 | March              ----+----------------      6 | one thousand
  4 | May                  3 | fourth             ----+-------------------
  4 | June                 3 | fourteenth           7 | seven thousand
  4 | July               ----+----------------    ----+-------------------
----+----------------      5 | ninth                8 | six thousand
  5 | October              5 | nineteenth         ----+-------------------
  5 | November           ----+----------------      9 | three thousand
----+----------------      6 | second             ----+-------------------
  6 | September          ----+----------------     10 | two thousand
                           7 | seventh
                           7 | seventeenth
                         ----+----------------
                           8 | third
                           8 | sixth
                           8 | tenth
                           8 | thirteenth
                           8 | sixteenth
                           8 | thirtieth
                           8 | thirty-first
                         ----+----------------
                           9 | twelfth
                           9 | twentieth
                           9 | twenty-*