Vyxal D, infinite score, 17 bytes

`ȧ$⌈ż꘍vq‛DĖ+⁋ `DĖ

Try it Online! The space near the end is significant insignificant whitespace.

`            `DĖ # Evaluate the following, on a stack containing two copies of itself:
   ⌈             # Split on spaces - iteration N includes N spaces, so this has length N+1
    ż            # [1, 2, ..., ^.length] i.e. [1, 2, ..., N+1]
     ꘍           # Over each of these, append that many spaces to
 ȧ$              # The other copy of the string, with whitespace removed
      vq         # Quote each,
        ‛DĖ+     # Append "DĖ" to each
            ⁋    # And join by newlines

Julia 1.0, infinite score, 69 bytes

(c=1;a=:(println.("(c=$(i);a=:($(a)))|>eval" for i = 1:c + 1)))|>eval

Try it online!

Ruby, infinite, 59 bytes

Updated:

eval$a=%q[2.times{|i|puts"eval$a=%q[#{i+2}#{$a[-46..]}]"}]

Previous (66 bytes):

eval$a=%q[2.times{|i|puts"eval$a=%q[#{$a.sub /^\d+/,"#{i+2}"}]"}]