I also wasn't sure what you mean by "texts" for total beginners.
If a textbook would suit your purpose (and since you prefer non-Hepburn romanization), you might like _Japanese The Spoken Language_ published by Yale (by Eleanor Hart.) It has more detailed grammar explanations than most [but be prepared for] some unique terminology. I think the audio is available on one of the univ websites.
There are a number of elementary textbooks and materials that include romaji. They usually contain basic dialogues, sentences and sometimes short readings. Japan Times used to publish one called something like _Modern Japanese_ . Most use Hepburn, I think. (All of the ones listed above?)
If it's longer texts you're after, I recall that a couple societies promoting the elimination of kanji had produced material intended for native speakers in kana-only or in romaji. Probably not appropriate for beginners, though. And the older stuff might contain some outdated Japanese.
fyi, I noticed
this site has a beta Japanese-to-romaji converter for sentences. It can't determine the correct kanji readings if there are alternate readings. [It lists the possibilities instead.]
But.... (jumping on the bandwagon) :-) ... I also wouldn't recommend using romaji. As I see it, there are no benefits and several disadvantages.
[fixed link and mangled sentence]
Edited: 2012-05-27, 1:29 am