@spelling of doubled consonants

When a consonant sound lasts more than usual, it is written twice.

Conversely, when a consonant is written twice, that does not mean that the movement is done twice — it just means that the tongue is held at the point of contact for a longer time. All consonants can be doubled, except r र्. Examples —

bhagavattama- भगवत्तमॱ "holiest", with a lengthened t त् sound written as t त् + t त्.

If the consonant is one of the ten aspirated consonants, instead of writting it twice, it is written as the most alike unaspirated followed by the aspirated —

vidyuc chobhate विद्युच्छोभते "lightning is flashing", with a lengthened ch छ् written as c च् + ch छ्.

Notice that the spelling rule applies even if when the merge consonants belong to different words and even if they are written with a space in between. So in —

on namaz zivAya ओं नमः शिवाय

there is a single lengthened z श् sound, and pronouncing that as two normal z श् sounds separated by a pause is ungrammatical. When you say a pause between those two eords, the pronunciation is namaH | zivAya || नमः । शिवाय ॥.

Why is r र् never doubled?

Doubling usually happens when two like consonants come together, so in bhagavattama- भगवत्तमॱ we have a lengthened t त् sound because the t त् of /tamap comes after the t त् of bhagavat भगवत्. This process never joins two r र् because rori and other rules prevent it — punA ramate पुना रमते.

Yet, the doubling rules do work in the absence of conjunction of like consonants. Won't any of those ever make a lengthened r र् sound?

No, they won't. None of those ever applies to r र्. Check them one by one.