The uncompressed string (with # replaced with \n for clarity) is:

!!!-. ! |:! |:!-' !!!
!!!~.--------. !~|        |:!~|        |:!~'--------' !!!
!!!~~~~~~~~~~.--------.!~~~~~~~~~~|        |!~~~~~~~~~~|        |!~~~~~~~~~~'--------'!!!
!!-------.   !       | '.!       |  |!       |  |!       | .'!-------'   !!
!!~~~~~~~.--------------.!~~~~~~~|              |!~~~~~~~|              |!~~~~~~~|              |!~~~~~~~|              |!~~~~~~~'--------------'!!
__      !  |'.   !  |   '.!  |    |!  |    |!  |    |!  |    |!  |   .'!__|.'   !
~~ ________________________ !~~|                        |!~~|                        |!~~|                        |!~~|                        |!~~|                        |!~~|                        |!~~|                        |!~~|________________________|!
'. !  |!  |!  |!  |!  |!  |!  |!  |!.' 

This encodes the left-side versions of the different screen components with ! instead of newlines, and ~ instead of ?, which are then right-padded with ~ to 30 characters before having themselves and their line-reversals added to a lookup list.

The rest of the code simply handles coordinate lookup with out-of-bounds cases ignored.

Clean (with Snappy), 800 785 670 644 bytes

460 402 bytes of code + 360 242-byte string literal
(escaped here and on TIO because it isn't valid UTF-8)

You can verify the length of the literal here.

import StdEnv,Data.List,Data.Maybe,Codec.Compression.Snappy,Text
@a b|b<'~'=b=a
$m x y d=map(@' ')(foldl(\a b=[@u v\\u<-a&v<-b])['~~'..][join['
']k\\Just(Just 1)<-[mapMaybe(\e=e!?(x+[u,v,~u,~v]!!d))(m!?(y+[~v,u,v,~u]!!d))\\u<-[-2,2,-1,1,0,-1,1,0,-1,1,0,-1,1]&v<-[3,3,3,3,3,2,2,2,1,1,1,0,0]]&k<-nub[q\\w<-split"#"(snappy_uncompress"\211\6\44\41\41\41\55\56\40\41\40\174\72\5\4\60\55\47\40\41\41\41\43\41\41\41\176\56\55\r\1\24\56\40\41\176\174\40\r\1\4\174\72\72\r\0\0\47\r\46\35\72\25\1\31\103\0\41\25\24\35\113\176\25\0\31\133\11\224\r\152\20\56\40\40\40\41\21\217\10\40\47\56\31\14\4\40\174\126\14\0\4\56\47\21\74\0\47\1\74\1\340\r\220\25\242\11\1\25\250\25\360\11\1\25\253\376\30\0\21\30\25\333\11\1\24\47\41\41\43\137\137\11\154\20\41\40\40\174\47\r\344\1\157\5\341\1\11\5\336\172\11\0\34\56\47\41\137\137\174\56\47\1\347\20\43\176\176\40\137\132\1\0\4\40\41\75\211\76\1\0\1\356\5\150\116\1\0\376\35\0\376\35\0\126\35\0\132\347\0\20\137\174\41\43\47\101\337\51\74\41\133\122\4\0\10\56\47\40"),q<-let l=[[c\\c<-:rpad s 30'~']\\s<-split"!"w]in[l,map reverse l]]])

Try it online!

Snappy compression actually does pretty well in this case, despite being speed-focused, because there are so many single-character runs in the string being compressed.

Clean (with Snappy), 800 785 670 644 bytes

460 402 bytes of code + 360 242-byte string literal
(escaped here and on TIO because it isn't valid UTF-8)

You can verify the length of the literal here.

import StdEnv,Data.List,Data.Maybe,Codec.Compression.Snappy,Text
@a b|b<'~'=b=a
$m x y d=map(@' ')(foldl(\a b=[@u v\\u<-a&v<-b])['~~'..][join['
']k\\Just(Just 1)<-[mapMaybe(\e=e!?(x+[u,v,~u,~v]!!d))(m!?(y+[~v,u,v,~u]!!d))\\u<-[-2,2,-1,1,0,-1,1,0,-1,1,0,-1,1]&v<-[3,3,3,3,3,2,2,2,1,1,1,0,0]]&k<-nub[q\\w<-split"#"(snappy_uncompress"\211\6\44\41\41\41\55\56\40\41\40\174\72\5\4\60\55\47\40\41\41\41\43\41\41\41\176\56\55\r\1\24\56\40\41\176\174\40\r\1\4\174\72\72\r\0\0\47\r\46\35\72\25\1\31\103\0\41\25\24\35\113\176\25\0\31\133\11\224\r\152\20\56\40\40\40\41\21\217\10\40\47\56\31\14\4\40\174\126\14\0\4\56\47\21\74\0\47\1\74\1\340\r\220\25\242\11\1\25\250\25\360\11\1\25\253\376\30\0\21\30\25\333\11\1\24\47\41\41\43\137\137\11\154\20\41\40\40\174\47\r\344\1\157\5\341\1\11\5\336\172\11\0\34\56\47\41\137\137\174\56\47\1\347\20\43\176\176\40\137\132\1\0\4\40\41\75\211\76\1\0\1\356\5\150\116\1\0\376\35\0\376\35\0\126\35\0\132\347\0\20\137\174\41\43\47\101\337\51\74\41\133\122\4\0\10\56\47\40"),q<-let l=[[c\\c<-:rpad s 30'~']\\s<-split"!"w]in[l,map reverse l]]])

Try it online!

Snappy compression actually does pretty well in this case, despite being speed-focused, because there are so many single-character runs in the string being compressed.

Clean (with Snappy), 800 785 670 645 bytes

460 377 bytes of code + 360 242-byte string literal
(escaped here and on TIO because it isn't valid UTF-8)

You can verify the length of the literal here.

import StdEnv,Data.List,Data.Maybe,Codec.Compression.Snappy,Text
@a b|b=='?'=a=b
$m x y d=map(@' ')(foldl(\a b=[@u v\\u<-a&v<-b])['??'..][join['
']k\\Just(Just 1)<-[mapMaybe(\e=e!?(x+[u,v,~u,~v]!!d))(m!?(y+[~v,u,v,~u]!!d))\\u<-[-2,2,-1,1,0,-1,1,0,-1,1,0,-1,1]&v<-[3,3,3,3,3,2,2,2,1,1,1,0,0]]&k<-nub[q\\w<-split"#"(snappy_uncompress"\211\6\44\41\41\41\55\56\40\41\40\174\72\5\4\60\55\47\40\41\41\41\43\41\41\41\77\56\55\r\1\24\56\40\41\77\174\40\r\1\4\174\72\72\r\0\0\47\r\46\35\72\25\1\31\103\0\41\25\24\35\113\176\25\0\31\133\11\224\r\152\20\56\40\40\40\41\21\217\10\40\47\56\31\14\4\40\174\126\14\0\4\56\47\21\74\0\47\1\74\1\340\r\220\25\242\11\1\25\250\25\360\11\1\25\253\376\30\0\21\30\25\333\11\1\24\47\41\41\43\137\137\11\154\20\41\40\40\174\47\r\344\1\157\5\341\1\11\5\336\172\11\0\34\56\47\41\137\137\174\56\47\1\347\20\43\77\77\40\137\132\1\0\4\40\41\75\211\76\1\0\1\356\5\150\116\1\0\376\35\0\376\35\0\126\35\0\132\347\0\20\137\174\41\43\47\101\337\51\74\41\133\122\4\0\10\56\47\40"),q<-let l=[[c\\c<-:rpad s 30'?']\\s<-split"!"w]in[l,map reverse l]]])

Try it online!

Snappy compression actually does pretty well in this case, despite being speed-focused, because there are so many single-character runs in the string being compressed.

Clean (with Snappy), 800 785 670 644 bytes

460 402 bytes of code + 360 242-byte string literal
(escaped here and on TIO because it isn't valid UTF-8)

You can verify the length of the literal here.

import StdEnv,Data.List,Data.Maybe,Codec.Compression.Snappy,Text
@a b|b<'~'=b=a
$m x y d=map(@' ')(foldl(\a b=[@u v\\u<-a&v<-b])['~~'..][join['
']k\\Just(Just 1)<-[mapMaybe(\e=e!?(x+[u,v,~u,~v]!!d))(m!?(y+[~v,u,v,~u]!!d))\\u<-[-2,2,-1,1,0,-1,1,0,-1,1,0,-1,1]&v<-[3,3,3,3,3,2,2,2,1,1,1,0,0]]&k<-nub[q\\w<-split"#"(snappy_uncompress"\211\6\44\41\41\41\55\56\40\41\40\174\72\5\4\60\55\47\40\41\41\41\43\41\41\41\176\56\55\r\1\24\56\40\41\176\174\40\r\1\4\174\72\72\r\0\0\47\r\46\35\72\25\1\31\103\0\41\25\24\35\113\176\25\0\31\133\11\224\r\152\20\56\40\40\40\41\21\217\10\40\47\56\31\14\4\40\174\126\14\0\4\56\47\21\74\0\47\1\74\1\340\r\220\25\242\11\1\25\250\25\360\11\1\25\253\376\30\0\21\30\25\333\11\1\24\47\41\41\43\137\137\11\154\20\41\40\40\174\47\r\344\1\157\5\341\1\11\5\336\172\11\0\34\56\47\41\137\137\174\56\47\1\347\20\43\176\176\40\137\132\1\0\4\40\41\75\211\76\1\0\1\356\5\150\116\1\0\376\35\0\376\35\0\126\35\0\132\347\0\20\137\174\41\43\47\101\337\51\74\41\133\122\4\0\10\56\47\40"),q<-let l=[[c\\c<-:rpad s 30'~']\\s<-split"!"w]in[l,map reverse l]]])

Try it online!

Snappy compression actually does pretty well in this case, despite being speed-focused, because there are so many single-character runs in the string being compressed.