To answer your question directly: Yes, the transformation of कर्म (karma) to कल्म (kalma) in the etymology of कल्मष (kalmaṣa) is indeed a classic application of the maxim रलयोरभेदः (ralayorabhedaḥ - the non-difference between 'r' and 'l'), which is formally accommodated in grammar by the exact Vārttika you cited.
To understand this comprehensively, we must look at the word कल्मष (kalmaṣa) from two distinct viewpoints: the Etymological (Nairukta/Semantic) perspective, which aligns with your findings, and the strict Pāṇinian morphological perspective.
1. The Etymological Perspective (Nairukta View)According to traditional etymologists (Nairuktas) and lexicons like the Vācaspatyam and Śabdakalpadruma, the word कल्मष (kalmaṣa - sin, dirt, stain) is derived precisely as you mentioned: कर्मन् (karman - action/merit) + √सो (so - to destroy)
"कपिलकादीनां संज्ञाछन्दसोर्वा रो लमापद्यत इति वक्तव्यम्॥ ... कर्म, कल्म। शुक्रः, शुक्लः।" (kapilakādīnāṃ saṃjñāchandasorvā ro lamāpadyata iti vaktavyam... karma, kalma. śukraḥ, śuklaḥ.) Translation: It should be stated that for the list of words beginning with 'kapilaka', the 'r' changes to 'l' in names and Vedic literature. (Examples:) karma becomes kalma, śukra becomes śukla.
While the above derivation is semantically beautiful, the strict Pāṇinian school often prefers to derive nouns using the Uṇādi Sūtras (a set of rules for words with irregular affixes).
According to this view, the word does not come from karma at all, but rather directly from a root that already has an 'l'.
Let us look at the word in the context of the verse you cited:
सर्वेऽप्येते यज्ञविदो यज्ञक्षपितकल्मषाः ॥ sarve'pyete yajñavido yajñakṣapitakalmaṣāḥ
Padaccheda (Word-Splitting): सर्वे (sarve) अपि (api) एते (ete) यज्ञ-विदः (yajña-vidaḥ) यज्ञ-क्षपित-कल्मषाः (yajña-kṣapita-kalmaṣāḥ).
Compound Parsing for यज्ञक्षपितकल्मषाः: यज्ञैः क्षपितम् (नाशितम्) कल्मषम् (पापं) येषां ते। (yajñaiḥ kṣapitam kalmaṣam yeṣāṃ te.) "Those whose sins (kalmaṣa) have been destroyed (kṣapita) by sacrifice (yajña)."
Philosophical Connection: If we adopt your etymological derivation (कर्म -> कल्मष), it adds a profound layer of meaning to Lord Krishna's words. The ultimate goal of doing Yajña (sacrifice) in the Gītā is Karma-yoga—acting without binding oneself to the fruits of action.
Therefore, Kalmaṣa is not merely "sin" in a Western moral sense, but represents the binding, tainting nature of Karma itself. By performing Yajña, the yogis destroy (kṣapita) the very actions (karma) that bind them to material existence.
In conclusion, your analysis is perfectly accurate. The transition from कर्म (karma) to कल्मष (kalmaṣa) via रलयोरभेदः is widely accepted by Sanskrit etymologists, heavily supported by the Vārttika under [Aṣṭādhyāyī 8.2.18], and adds beautiful philosophical depth to Gītā 4.30.