The following quote has also be found in Mīmāṃsākoṣa. I will complete its translation in the next days.
ākhyātopasthitā arthabhāvanā kiṃ kena kathaṃ ity aṃśatrayaṃ krameṇāpekṣamāṇā “kim iṣṭaṃ kuryāt” ityākāṅkṣāyāṃ yāgasya kaṣṭatvena karaṇatvena ca asādhyatayā “yāgena anyad bhāvayet” iti (uttaram). tataḥ “kim idaṃ tat anyat?” ityākāṅkṣāyāṃ svargakāmapadasamarpitaṃ asiddhatayā sādhanāpekṣaṃ svargam eva arthabhāvanā bhāvyatvena svīkaroti. śrutivṛttyā hi padārthabhūtasya svargakāmasya bhāvyatvam ucyamānaṃ viśeṣyabodhe viśeṣaṇe svarge paryavasyati. tathā ca yāgena svargaṃ bhāvayet iti phalitam. yāgakaraṇikā svargaphalikā pravṛttiḥ pravartanāviṣayaḥ iti bodhaḥ. yatra ca samabhivyāhṛtānupasthitaṃ phalaṃ tatra prakaraṇādinā teṣām apy abhāve arthavādena vidhisāpekṣeṇa (rātrisatreṣu), tasyāpy abhāve viśvajinnyāyena phalaviśeṣaḥ kalpyate. yady api puruṣapravṛttirūpabhāvanāniṣpādyo yāgaḥ tatra na karaṇaṃ, tathāpi phalāvacchinnabhāvanāyāṃ viśeṣaṇe karaṇatve (karaṇe) karaṇatvopacāraḥ iti phaloddeśyakapravartakakṛtiviṣayatvam eva atra karaṇatvam. daṇḍena ghataṃ karoti ityādau loke 'pi tathaiva karaṇatvam. kena ityāsyāpi kiṃviṣayiṇī kṛtiḥ svargasādhanaṃ ityarthaḥ ity anye. atra yāgakaraṇatvaviśiṣṭe lakṣaṇā iti prāñcaḥ. vastutaḥ karaṇatvaṃ yāgasya saṃbandho vākyārthaḥ. evaṃ jyotiṣṭomādes tatra abhedenānvayo nirābādhaḥ. itthaṃ ca kathaṃ vinaṣṭena yāgena svargo bhāvyaḥ iti pratītyanavasāne antarā apūrvaṃ kṛtvā iti saṃbadhyate. tataḥ “katham apūrvaṃ yāgena kartavyaṃ” iti apūrvabhāvanāyāṃ itthaṃbhāvena saṃyujyamānam itikartavyatājātaṃ apūrvaprayuktam ity ucyate. tataḥ prakārāpekṣāyāṃ “samidho yajati” ityādivākyaiḥ iṣṭaviśeṣāpekṣaiḥ svādhikāravākyaikavākyatayā “darśapūrṇamāsabhāvanā prayājādibhāvanopetā apūrvaṃ sādhayati” ity avagate prayājādīnāṃ tādarthyena samanvaye paścāt upakāratvaṃ (upakārakatvaṃ) kalpyate. tad ayaṃ bhāṭṭamate bodhakramaḥ. “svargakāmaniṣṭhā yāgakaraṇikā svargaphalikā prayājādītikartavyatākā bhāvanā” ity arthabhāvanābodhaḥ. “vidhiniṣṭhā śaktigrahakaraṇikā stutyarthavādopakṛtā pravartanā” iti śabdabhāvanābodhaḥ śaktikalpanena lakṣaṇayā vā upapadyate. tato 'varuddhā arthabhāvanā niruktapravartanāviṣayaḥ ity ekavākyatayā mahāvākyārthabodhaḥ. ata eva vidhyuparaktā bhāvanā liṅarthaḥ iti bhāṭṭasiddhāntaḥ. vidhiḥ pravartanā taduparaktā tadviśiṣṭā arthabhāvanā liṅpratipādyā ity arthaḥ. arthabhāvanāviśeṣaṇatvenaiva śabdabhāvanāyā anvayaḥ rājādikṛtājñādeḥ tathaivānvayāt. tadanvayena yogyatvena pravartanāyām api balavadaniṣṭhānanubandhīṣṭasādhanatvaṃ labhyate. “na surāṃ pibet” ityādau pratiṣedhavākyārtho 'pi ittham evonneyaḥ evam anye 'pi anvayabodhāḥ svayamūhyāḥ iti. (Mīmāṃsācintāmaṇi, pp. 92-93).
Approximate translation (for the time being, I did not polish the English form of this translation, which is only meant as a guide-line through the Sanskrit text):
The arthabhāvanā lead [to the listener] by verbal forms (ākhyāta), expects three components [answering], in due order [the following questions] “What [has to be brought about]?”, “By means of what?” and “In which way?”
As for the expectation “Which desirable [thing] should one do?”, since the sacrifice cannot be the thing to be realised, since it is [by itself not desirable at all, but rather] grievous, and since it is instrumental, the answer is “through the sacrifice, one should cause to be something else”. Hence, [when one asks] “What is this other [thing]?”, since [heaven] has not been accomplished and needs an instrument to be realised, the bhāvanā accepts heaven alone, delivered by the word «the one who is desirous of heaven» [in the prescription «The one who is desirous of heaven should sacrifice with the Full and New Moon Sacrifices»], as the thing it has to cause to be. […] Hence, the [prescription] ends up by meaning “through the sacrifice, one should cause to be heaven”.
I have no keys as for prāñca. Who are those “Eastern” Mīmāṃsakas?
Besides the problem of arthabhāvanā, it is impressive how such analyses of arthabhāvanā and its components are common throughout Bhāṭṭa texts. I read similar depictions in the Bhāṭṭa pūrvapakṣinaḥ of Rāmānujācārya's Tantrarahasya as well as in Āpadeva's Mīmāṃsānyāyaprakāśa and so on.