So sings the madam of a Viennese brothel in the Sherlock Holmes pastiche The Seven-Per-Cent Solution. Would-be sleuths should adopt a similar philosophy when entering answers into the grid; this will result in modifications to many answers, all yielding alternate words.

Across and Down grid entries comprise a total of 200 letters. Of these, 14 letters make up a final "seven-per-cent" solution. Transferring the initial letters of the indicated grid entries into the blanks below the grid will reveal what's required to solve this puzzle.

ACROSS

3 Physical appearances seem ultimately warped into fantasies

9 Outspoken Asian's no-win situation

10 Ridiculous acronym includes "H" for "bHutan"; e.g.

11 Our tutors contrived to be painfully exacting

13 Doctor sees papa making attempts to be conciliatory

15 British nobleman embracing very quiet season

17 Freak finally creating a tattoo is twisting awkwardly

19 Codger snared in Social Security hustles

20 Ribs I mixed with beer; they might get palms greasy?

22 Five hundred and four competed, separated into groups

25 A quick assessment of ethics tells me all about "saint" (2 wds)

26 Find a nice part for a guy in Joseph and the Amazing Technicolor Dreamcoat

27 Superman's nemesis is badly hurt; Lois is missing

28 Offensive ad needed to be blunted

29 Thus, Department of Defense rebuffed numbskulls

33 Oddly modest health care providers (abbr)

35 Hairspray character entering at first and heading stage right

36 Works to make perfect almost like Abe Lincoln

39 Epic prices: unfortunately they can be quite steep

40 Alternating members of theatre cast led the intimate discussion (hyph)

41 Ineptly narrate hodgepodge describing some space travel

DOWN

1 Chiefly semiarid, treeless ecoregions (plains, prairies, even shrublands)! …