C (clang), Score 678 675 669 (312 bytes)

*a[]={">[>]+<[+<]>>>>>>>>>[+]<<<<<<<<<",">,>,>,>,>,>,>,>,<<<<<<<<",">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+]<<<<<<<<<",">;>;>;>;>;>;>;>;<<<<<<<<","<<<<<<<<<",">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+<<<<<<<<[>]+<[+<]",">>>>>>>>>",">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>]<[+<]"};f(s[]){for(;*s;)printf(a[*s++%43%13]);}

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Inspired by @Arnauld's JavaScript answer.

Changed the index calculation to n % 43 % 13 to avoid empty strings in the dictionary thus saving a whopping 3 points from the score =)

JavaScript (ES7), Score:  492  485

The scoring scheme makes most compression attempts counter-productive. So what we really want to do is just use as few expensive characters as possible... ¯\_(ツ)_/¯

Expects an array of ASCII codes.

a=>a.map(c=>[[">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>"][8>>c**7]]+`[+<<<<<<<<[>]+<[+<]--]<[+<]-->[>]+<[+<]>>>>>>>>>[+]<<<<<<<<<->,>,>,>,>,>,>,>,<<<<<<<<-[+]<<<<<<<<<->;>;>;>;>;>;>;>;<<<<<<<<-<<<<<<<<<-->>>>>>>>>`.split`-`[c%13]).join``

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05AB1E, score 292 (166 bytes)

“>-+.+[>+]<[<]>-[+.[>]+<[+<]-->-+.+[>+]<[<]>-]<[+<]-->[>]+<[+<]>-[+].<->,>,>,>,>,>,>,>,.->-+.+[>+]<[<]>-[+].<->;>;>;>;>;>;>;>;.-.<-->-“„>-¬9×:'.“<<<<<<<<“:'-¡IT>>>%èJ

Port of @Arnauld's first JavaScript answer, with some additional score improvements by using replaces.

Input as a list of code-point integers.

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Explanation:

“>-+…>-“               # Push this string
        „>-            # Push ">-"
           ¬           # Push its first character without popping: ">"
            9×         # Repeat it 9 times: ">>>>>>>>>"
              :        # Replace all ">-" with ">>>>>>>>>" in the big string
        '.            '# Push "."
          “<<<<<<<<“   # Push "<<<<<<<<"
                    :  # Replace all "." with "<<<<<<<<" in the big string
        '-¡           '# Then split on "-"
           I           # Push the input-list of codepoint-integers
            T          # Push 10
             >>>       # Increase it three times to 13
                %      # Modulo
                 è     # 0-based index each into the list of strings
                  J    # Join this list to a single string
                       # (which is output implicitly as result)

Charcoal, 160 bytes, score 265

⭆Ｓ§⪪⪫⪪⪫⪪-+.+[>+]<[<]-[+.[>]+<[+<]++++-+.+[>+]<[<]-]<[+<]++++>[>]+<[+<]-[+].<++>,>,>,>,>,>,>,>,.++-+.+[>+]<[<]-[+].<++>;>;>;>;>;>;>;>;.++.<++++-++++¦-×>⁹.×<⁸++℅ι

Attempt This Online! Link is to verbose version of code. Explanation: Port of @Arnauld's JavaScript answer, but modified using @Ausername's compression.

 Ｓ                      Input string
⭆                       Map over characters and join
        ...             Translation string
      ⪫⪪   -×>⁹         Replace `-` with nine `>`s
    ⪫⪪         .×<⁸     Replace `.` with eight `<`s
   ⪪               ++   Split on literal string `++`
  §                     Indexed by
                      ι Current character
                     ℅  Ordinal
                        Implicitly print

JavaScript (Node.js), 503 score

f=([c,...a])=>c?`;+>[>]+<[+<]>>>>>>>>>[+]<<<<<<<<<;+;->>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+]<<<<<<<<<;-;<<<<<<<<<<;<;>>>>>>>>>>;>;,>,>,>,>,>,>,>,>,<<<<<<<<;,;.>.>.>.>.>.>.>.>.<<<<<<<<;.;[>>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+<<<<<<<<[>]+<[+<];[;]>>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>]<[+<]`.split(';'+c)[1]+f(a):[]

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Each map is surrounded by ;<char><mapped>;<char> to allow low-cost indicing

Funge-98, score 972

~:'+-!#[_>:'--!>#]_>:'<-!>#[_>:'>-!#[_>:',-!#[_>:'.-!>>#]_>:'[-!>>>>>>>#]_']-!#]_>
]].....[$"<<<<<<<<<]+[>>>>>>>>>]<+[<+]>[>";..[$"<<<<<<<<,>,>,>,>,>,>,>,>"#;
[<...............]$"<<<<<<<<<]++-[>>+->>>>>>>]<[<]+>[+<<<<<<<<+>>>>>>>>>">
[<<<<<<<<<<<<<<<;+;<<<<<<<<<:k7<<<<<]...................]$"<<<<<<<<;>;>;>;>;>;>;>;>"
>,:1j2_]<<">>>>>>+->>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+<<<<<+-<<<[>]+<[+<]"$[
<<<<<<<]<<<<<<<<;+;<<<<<<<<<<<<">>>>>>>>>+<<<<<<<<+[>+]<+-[<]>>>>>>+->>>]<[+<]"<.]

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The program never halts, so if you run it using TIO, you have to manually cancel execution in order to view the output.

Google Sheets, score 610

=switch(A1,"+",">[>]+<[+<]>>>>>>>>>[+]<<<<<<<<<","-",">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+]<<<<<<<<<","<","<<<<<<<<<",">",">>>>>>>>>",",",">,>,>,>,>,>,>,>,<<<<<<<<",".",">;>;>;>;>;>;>;>;<<<<<<<<","[",">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+<<<<<<<<[>]+<[+<]","]",">>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>]<[+<]")

Dumb solution, compression doesn't seem to pay because of the scoring system.

Vyxal, 156 bytes, score 247

kT`;>+-+[>+]<[<];>[+-[>]+<[+<]++;>+-+[>+]<[<];>]<[+<]++-<++;>++;>+-+[>+]<[<];>[+]-<++>[>]+<[+<];>[+]-<++>.>.>.>.>.>.>.>.-++>,>,>,>,>,>,>,>,-`‛-;‛<>f8*Ŀ‛++/Ŀ

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There's not much room for optimisation here, because any trick has to save eight times the cost of the program encoding it. So, all this does is replace long runs of > and < with - and ;, and separate builtins with ++, then replace the corresponding commands.

For a shorter but worse-scoring solution:

Vyxal, 76 bytes, score 601

kT«Wėm¦n½LøsJƒ›WǎQøḢi‹WK⇩f↑¼,uṪ∑¥↳₁ṡ²₈>⊍₌?-₀O∷×Ḟ•ṫ¼i8#S⇧⌐«n8ẎkTĿn∷9Ẏ(n/ṫj)⌈Ŀ

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A more compressed approach that doesn't really work with the custom scoring. This uses various regpack-based compression tricks and it's a bit of a mess.