First of all, Modern Sinhala means the language spoken in the current time period. If a word comes from Modern Sinhala, it means it is used in the modern language, it does not imply that the word has a modern etymology, i.e. is a recent invention.
My take on the word artha අර්ථ is that it is a Sanskrit loanword (cf. Hindi artha)corresponding to the native Elu word aruta අරුත and possibly ata අත.
I. Let us have a look at definite Sanskrit borrowings in the Modern Sinhala, e.g. sthavira ස්ථවිර . First, we know for sure that the th in sthavira is pronounced as an aspirated dental plosive in Sanskrit and Vedic. How do we know it? Because of the oral transmission of the Vedas and Sanskritic literature among the Brahmins, conserving the ancient pronunciation. I think you would agree that it is not plausible that the Europeans made the entire India use the incorrect pronunciation for their 3,500 years old sacred tradition. At the same time, Modern Sinhala, and any native speaker can correct me if I am wrong, doesn’t aspirate t in sthavira, so the akṣara tha ථ is actually pronounced as [t̪a], so sometimes one comes across the incorrect spelling ස්තවිර.
II. If we look at other Sanskrit borrowings in Modern Sinhala like dharmaya ධර්මය, sthāna ස්ථාන, saṁkhyā සංඛ්යා and lots and lots of other loanwords, we will see them systematically featuring miśra characters totally useless in Sinhala, and occurring in corresponding Pali words where they can be predicted (for rules of transition between Sanskrit and Pali I would recommend Geiger’s Grammar of Pali): bhikkhu භික්ඛු , Buddha බුද්ධ, dukkha දුක්ඛ, dhamma ධම්ම and, yes, attha අත්ථ. This spelling is consistently observed across all recensions of the Pali Canon, the Thai, Burmese, Lao and Khmer versions. I have found no information on any widespread confusion among Sinhala scribes as to which akṣaras to use in these words in Pali texts, ත or ථ, බ or භ, ක or ඛ. If you find any contradicting information on it, great, I will be happy to study the matter in more depth.
III. The ‘naturalized’ Prakrit words feature exclusively śuddha akṣaras: aṭa අට (cf. Pali aṭṭha අට්ඨ and not *අට්ට), Budu dahama බුදු දහම (cf. Pali Buddhadhamma බුද්ධධම්ම or Sanskrit Buddhadharma බුද්ධධර්ම), bik බික් (see the picture below: cf. Pali bhikkhu භික්ඛු, Sanskrit loanword bhikṣuwa භික්ෂුව), tera තෙර (cf. Pali thera ථෙර), aruta අරුත (and ata අත?) (cf. to Pali attha අත්ථ, Sanskrit artha අර්ථ).
IV. So, Sanskrit words always have aspirated miśra akṣaras that we know to be aspirated dental plosives, the Pali words have aspirated miśra akṣaras whenever predicted by the form of the Vedic or Sanskrit word in all scripts the Pali Tipitaka is preserved in (e.g. aṣṭa > aṭṭha > අට්ඨ( > Sinh aṭa > අට)). The Elu words have no miśra akṣaras. There is to my knowledge little confusion in the use of śuddha and miśra akṣaras in the extant Pali texts and / or manuscripts (no *බික්ඛු or *දම්ම), if you know any apart from the hypothetical atta / attha, feel free to share the news 
Thus, it is quite difficult to imagine that the scribes or reciters could have confused attā and attha and not done it with all the derived words and other words featuring aspirated consonants in Pali.
V. Last but not least, the Pali word attha අත්ථ is actually masculine or neutral, which makes the hypothetical *Rūpaṃ … anatthā රූපං … අනත්ථා a grammatical impossibility unless it is in Ablative (very unlikely), and the hypothetical *atthatthā අත්ථත්ථා in SN 44.10 would be completely impossible under all grammatical circumstances - as far as I can see. The correct form would have been either Rūpaṃ … anattho රූපං … අනත්ථො or Rūpaṃ … anatthaṃ රූපං … අනත්ථං - and I do not find it anywhere in the Anattalakkhana Sutta.
Sorry, I could go on, but it is too late, I have already spent hours on research and I have to get up early tomorrow. However, I learned a lot about Sinhala today - the Sinhala script is awesome, so beautiful! - thanks for giving me this opportunity, it was totally worth it 