Browsing the Web through unlimited SMS plan
A week later, I found what I was looking for. After playing around with Google Voice and SMS APIs, I stumbled across an online service that offers exactly what I want, for free.

It's called txtWeb, and consists of just messaging 898-932 with your command, ex. @www YouTube.com returns:

(X)
(Y)Upload
* Home

* (Z)Trending
* 
      o (X) Home
      o (Z) Trending
  -----
* Best of YouTube

      o (A) Music
      o (B) Sports
      o (C) Gaming
      o (D) Movies
      o (E) TV Shows
      o (F) News
      o (G) Live
      o (H) Spotlight
      o (I) 360° Video
  -----
* 
      o (J) Browse channels
  -----
* Sign in now to see your 
channels and recommendations!

  (K)Sign in
  -----
* 
      o (L) YouTube Red
 (N) Show ad...&lt;br/&gt;&lt;br/&gt;
Reply M for more&lt;br/&gt;---&lt;br/&gt;&lt;
br/&gt;&lt;br/&gt;&lt;/body&gt;&lt;/html&gt;


Which is a bit outrageous but fulfills exactly what I needed.

Other commands include @wikipedia [query], or @daak, which offers a rudimentary email checking interface for gmail.

Fun.