have you come across the infinitive used as the subject of finite verbs in Sanskrit? 

It is the way Rudrabhaṭṭa seems to use it in Śṛṅgāratilaka 1.116d* (p. 31 of Pischel's edition):

āstāṃ rantum aho nirīkṣitum api preyān na sambhāvitaḥ ||

Anvaya: preyān nirīkṣituṃ na sambhāvito rantum āstām. 

Rough English tr.: The beloved was not honoured to be looked at, forget about making love. 

Is this kind of construction fully acceptable? 

The Śṛṅgāratilaka commentator Gopālabhaṭṭa does not address the matter.

Speijer (pp. 306-307) declares that the infinitive "nowhere serves to express the subject, predicate or object of a sentence", but in note 1 on p. 307 he adds: "in such expressions as vidyate bhoktum, labhate bhoktum we may speak of the infinitive as the subject and object of the finite verb, but this is so only from a logical point of view; and it is, indeed, not considered so by Sanskrit-speakers". 

I would be of course very grateful for references, etc. 

All the best, 

Gaia Pintucci

PS: *Here for the sake of completeness you have 116a-c: 

mīlanmantharacakṣuṣā paripatatkāñcīgrahavyagrayā 

gāḍhānaṅgabharasravajjaghabayā kampoparuddhāṅgayā | 

sarvāṅgaiś caṭukārako 'py abalayā saṅketake kautukād