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##Seriously, 43 bytes

6╙¬▀'_+,;)-@s`;0@Eùk`M┬i;╗;lrZ`i@╜í=`M@░' j

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The lack of regex capabilities made this much more difficult than it needed to be.

Explanation:

6╙¬▀'_+,;)-@s`;0@Eùk`M┬i;╗;lrZ`i@╜í=`M@░' j
6╙¬▀ push digits in base 62 (uppercase and lowercase letters and numbers)
 '_+ prepend underscore
 ,;) push two copies of input, move one to bottom of stack
 - get all characters in input that are not letters, numbers, or underscores
 @s split input on all occurrences of non-word characters
 `;0@Eùk`M for each word: push the first letter (lowercased)
 ┬i transpose and flatten (TOS is list of first letters, then list of words)
 ;╗ push a copy of the first letters list to register 0
 ;lrZ zip the list of first letters with their positions in the list
 `i@╜í=`M for each first letter: push 1 if that is the first time the letter has been encountered (first index of the letter matches its own index) else 0
 @░ filter words (take words where corresponding element in the previous list is truthy)
 ' j join on spaces