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The answer is a six-letter word. You're strongly encouraged to discuss and collaborate on the puzzle in this chat room.

I've had this puzzle playtested before, but I still welcome feedback and suggestions.

1) Diamond, to carbon  
2) Deflated (#7)  
3) That in “this or that” (#9)  
4) Eureka producer (#6)  
5) Elevated beard (#8)  
6) Old-school marksmen (#2)  
7) Take to court (#4)  
8) Like flashlight bulb (#7)  

=

70’s fever (#3 of 5)  
Apportion (#4 of 5)  
Have to (#4 of 4)  
Not poetry (#2 of 5)  
Piece of curve (#1 of 3)  
Pizarro victim (5)  
Sing through nose (#2 of 3)  
Tweak (#5 of 5)  

+

American before America (#2 of 6)  
Back or head problem (#2 of 4)  
Climber’s way back (#1 of 7)  
Hitchcock thriller (#3 of 4)  
Like kittens (#4 of 4)  
Lost some fluid (4)  
Quite (#3 of 4)  
That woman’s (#1 of 4)  
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That was a very, very nice puzzle! Solved this with a lot of help from @grc

Here's a step-by-step walkthrough of how we solved it.

Working out some clues

We figured that (#X of Y) probably meant that the clue answer had Y letters, and that we had to take the X-th letter later. Why some clues didn't have a #X we weren't sure, but the first clues we worked out were the following:

70's fever               DISCO
Apportion
Have to                  MUST
Not poetry               PROSE
Piece of curve           ARC
Pizarro victim
Sing through nose        HUM
Tweak<br>
American before America
Back or head problem     ACHE
Climber's way back       DESCENT
Hitchcock thriller       ROPE
Like kittens
Lost some fluid
Quite
That woman's             HERS

Figuring out the mechanic

From the clues we had, we worked out that MUST + ACHE = MUSTACHE, which is indeed an "elevated beard". This makes sense, given the + and = in the puzzle, and made it easier to work out the remaining clues.

Filling in the rest

The remaining clues could then be filled in like so:

Diamond, to carbon       ALLOT + ROPE
Deflated                 HUM   + BLED
That in "this or that"   ALTER + NATIVE
Eureka producer          DISCO + VERY
Elevated beard           MUST  + ACHE
Old-school marksmen      ARC   + HERS
Take to court            PROSE + CUTE
Like flashlight bulb     INCAN + DESCENT
70's fever               DISCO
Apportion                ALLOT
Have to                  MUST
Not poetry               PROSE
Piece of curve           ARC
Pizarro victim           INCAN
Sing through nose        HUM
Tweak                    ALTER
American before America  NATIVE
Back or head problem     ACHE
Climber's way back       DESCENT
Hitchcock thriller       ROPE
Like kittens             CUTE
Lost some fluid          BLED
Quite                    VERY
That woman's             HERS

Taking letters

If we take the letters of the first set of clues as indicated (e.g. Deflated (#7) means to take the 7th letter of HUMBLED, or D), then we get DIVERSE. Note that the first clue, Diamond, to carbon, contributes no letters.

For the second and third sets, we do the same but in the order of the first set of clues, like so:

ALLOTROPE          ALLOT    O    ROPE    P
HUMBLED       D    HUM      U    BLED
ALTERNATIVE   I    ALTER    R    NATIVE  A
DISCOVERY     V    DISCO    S    VERY    R
MUSTACHE      E    MUST     T    ACHE    C
ARCHERS       R    ARC      A    HERS    H
PROSECUTE     S    PROSE    R    CUTE    E
INCANDESCENT  E    INCAN         DESCENT D

As you can see, we get OURSTAR and PARCHED.

The answer

So what do we do with DIVERSE, OURSTAR and PARCHED? We reapply the mechanic!
Our star is SUN and "parched" is DRY, so the answer, a word meaning "diverse" is...

SUN + DRY = SUNDRY
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