Just to clarify there is no word rastu (in Sanskrit). The word is astu, which is the 3rd person singular imperative of the verb √as 'to be' and means 'may there be, may it be'. This leaves us with siddhir, which we can see is the word siddhiḥ (nominative singular) meaning 'accomplishment, perfection'. It is affected by the sandhi rule that -iḥ followed by a vowel becomes -ir: hence siddhir astu 'may there be perfection'. Note that when we transliterate Sanskrit in Roman script we break the word between the consonant and the vowel. However in Devanāgarī the situation is more confusing because the whole thing is written as one word - the r and a are combined into a single akṣara : सिद्धिरस्तु the syllables being सि द्धि र स्तु (si ddhi ra stu). This is one of the disadvantages of Indic scripts, and part of what makes learning Sanskrit difficult. To read it you have to know the suffixes and sandhi rules very well.
This kind of mistake is quite common amongst Buddhists, i.e. the mistake of seeing a familiar word like siddhi, and breaking there, even when it produces non-sense words like rastu. It seems to have happened in Tibetan readings of the Vajrasattva mantra from the Sarvatathāgata-tattvasaṃgraha as well - as I discuss in my Western Buddhist Review article on the mantra: The Hundred Syllable Vajrasattva Mantra. The best example is the phrase sarvakarmasu ca me cittaṃ sreya kuru' and, in all actions make my mind more excellent' being read as sarva karma suca me cittaṃ śreya kuru, thereby obliterating the sense of the words, leaving words without any grammatical relationships, and creating the nonsense word suca. Basically it's what happens when you have a tradition in a language you don't speak.
This does not explain the form found on page 33 of John Stevens' Sacred Calligraphy of the East: siddhāṃrastu (which I have commented on before). But at least we can now see where it comes from. What was written on ancient Sanskrit manuscripts was not siddhāṃastu, or even siddhamastu, but siddhir astu.
Roth, Gustav. (1986) 'Mangala-symbols in Buddhist Sanskrit Manuscripts and Inscriptions' in Bhattacharya, G (ed.) Deyadharma : Studies in Memory of Dr D. C. Sircar. Sri Satguru Pubs. Delhi, p. 239-250.