My suggestion is that both phrases are most properly set in the accusative:
Hominem esse me delectat.
Finnum esse est canere.
I will break my argument into two steps:
- The accusativus cum infinitivo (AcI) can be used as a subject: this proves that the accusative case is not an "accidental" consequence of the fact that it is the object of such words as dicere, arbitrari, etc.
- The nominativus cum infinitivo (NcI) is used in a different context: the suggestive name requires an explanation.
The AcI as subject
Let us begin with Pinkster's examples in Oxford Latin Syntax:
In hac habitasse platea dictum'st Chrysidem. (Ter. An. 796)
Here, the subject is Chrysidem habitasse in hac platea: it is the thing that was said (dictum est).
Pinkster also advances:
...scalpellum adhiberi sine pernice non posse manifestum est. (Cels. 7.20.2)
...though this may be begging the question, since scalpellum is neuter and could thus be nominative or accusative.
A third example from Cicero:
Sed iam tempus est me ipsum a me amari.
A similar one from Plautus not cited by Pinkster:
Video. edepol nunc nos tempus est malas peioris fieri. (Pl. Mil. Glor. 1218)
Another common usage is as the subject of delectat or iuvat (as in the OP's first example sentence).
iuvitque me tibi cum summam humanitatem tum etiam tuas litteras profuisse. (Cic. Epist. ad Fam. 182)
What iuvit'ed? "tuas litteras profuisse"
Applied to your examples:
To justify my conclusion that the accusative should be used, here are two parallel examples that correspond fairly well to yours:
- hominem esse me delectat
Venit hoc mihi, Megadóre, in mentem, ted esse hominem divitem, factiosum, me autem esse hominem pauperum pauperrimum; nunc si filiam locassim meam tibi, in mentem venit te bovem esse et me esse asellum. (Pl. Aul. 227-230)
The me esse + acc. N + V seems a convincing parallel.
- Finnum esse est canere
One "last frontier" that is seldom crossed presents itself: Is the AcI ever used as the subject of esse? Cicero says yes:
Non est igitur amici talem esse in eum, qualis ille in se est, sed potius eniti et efficere, ut amici iacentem animum excitet inducatque spem cogitationemque meliorem. (Cic. Lael. de Amicit 59:5-8)
For those who have difficulty with the syntax, I would translate the first part as: "Therefore, it is not a friend's task to be the same towards [his friend] as he is towards himself." (Amended by @TKR's suggestion)
Function of the NcI
Although it is difficult to find a definitive resource, it appears that this construction falls into two classes: auxiliary verbs and passive verbs. Let's look at a few examples:
tárdus esse ílico coépi (Pl. Cas 885)
T. Mihin malum minitare? C. Atque edepol non minitabor, sed dabo,
mihi si perges mólestus esse. (Pl. Curc 572)
These verbs of "continuing," "beginning," or "ending" can take the infinitive + nominative. I will not cite examples of the most ubiquitous use case (which I'm not sure even qualifies as an NcI): volo and possum (et similia) + infinitive.
And now we get to an interesting case: Nom. + passive verb + Inf.
etenim cum artifex eius modi sit ut solus videatur dignus esse qui in scaena spectetur... (Cic. Quinc. 78.5)
risisse Cupido dicitur atque unum surripuisse pedem. (Ov. Amor 1.1.3-4)
Other passive examples (with fertur, vetatur, iubentur, etc.) abound.
The overwhelming consideration in my mind is that for "auxiliary verbs", the infinitive appears to be part of the verb itself (vult esse, coepi fieri, etc.), essentially functioning as one copulative. For passive verbs it is worth noting that the nominative is the subject of the passive verb--hence the nominative--and, to go out on a limb, the infinitive is added by way of analogy to the active construction.
Regardless, neither case seems to be met in your example sentences. Counter-examples in another answer/comments are very welcome!