I'm really interested to know of the Puranas which criticize the Pancharātra
Yes.
Several texts provide criticism for several philosophies of Vaishnavasim and other sects like Shaivism and Shaktism too. I'm giving references from two Puranas, not the ones though which have been "especially-asked for in the question".
- The Kurma Purana criticizes the Pancharatra, along with Jainas, Kapalikas, and Yamalas.
Kurma Purana 1.12.262
- They i.e., those contrary to the Vedas are the cults of Kapala, Bhairava, [Pancharatras], Yamala, Vama, and Arhata (Jaina).
- In another incarnation of mine, these scriptures have been promulgated by me to delude the people who themselves try to mislead
the other persons by propagating their false scriptures.
English Translation by Motilala Banarasidass Publications
- The Devi Bhagavata-Purana
Devi Bhagavatam 11.1
ये कुशास्त्राभियोगेन वर्तयन्तीह मानवान् ॥ २९ ॥ अधोमुखोर्ध्वपादास्ते
यास्यन्ति नरकार्णवम् । कामाचाराः पाशुपतास्तथा वै लिङ्गधारिणः ॥ ३० ॥
तप्तमुद्राङ्किता ये च वैखानसमतानुगाः । ते सर्वे निरयं यान्ति
वेदमार्गबहिष्कृताः ॥ ३१ ॥ वेदोक्तमेव सद्धर्मं तस्मात्कुर्यान्नरः सदा ।
उत्थायोत्थाय बोद्धव्यं किं मयाद्य कृतं कृतम् ॥ ३२ ॥
Those who do injury to others even by the blade of a Kuśa grass used
as a weapon, go to hell with their heads downwards and their feet
upwards. Those that follow their own sweet free will, that take up any
sort of dress (e. g. Bauddhas), those that follow the philosophical
doctrines called Pāśupatas, and the other hermits and saints and
persons that take up other vows contrary to the religions of the
Vedas, for example, the Vaikhānasa followers, [those who brand their
bodies by the hot Mudrās], at the places of pilgrimages, e. g. Dvārkā,
etc., they go to hell with their bodies scorched by red hot brands
(Tapta Mudrās). So persons should act according to the excellent
religions commanded by the Vedas.
English Translation by Swami Vijnananda
Here, although Pancharatra is not directly criticized, I think, the reference to those who brand their bodies by the hot Mudrās points to the Pancharatrins only. Besides, another sect within Vaishnavism known as - Vaikhanasa has been along with others.