One who is not īśvara (anīśvaraḥ) should never imitate the behavior of īśvaras, even mentally. If out of foolishness an ordinary person does imitate such behavior, he will simply destroy himself, just as a person who is not Rudra would destroy himself if he tried to drink an ocean of poison.
In the Telugu translation of Bhagavatam of Potana (late 1400s), there is a mention of candra (moon) and vāsava (indra) as examples of īśvaras, in addition to Rudra as mentioned above.
Here are corresponding verses from the Telugu version:
10.1-1106 (Translation of 10.33.29)
sarvabhakṣuⁿ ḍagni sarvambu bhakṣiñci
dōṣigāni pagidi dōṣa mainaⁿ
jēsi dōṣapadamuⁿ jendaru tējasvu
laguṭaⁿ jandra vāsavāduⁿ ladhipa!
Meaning:As all-devouring fire remains unpolluted even after consuming everything, the same the spirited-people (tējasvi+lu) such as candra (moon) and vāsava (indra) remain untainted for their transgressions.
10.1-1107 (translation of: SB 10.33.30)
īśvaruⁿḍu gānivāⁿḍu na-
rēśvara! parakāntaⁿ dalaⁿci yeṭlu braduku? gau-
rīśvaruⁿḍu dakka nanyuⁿḍu
viśvabhayadaviṣamu mriṅgi velayaṅgalaⁿḍē?
Meaning: O King (narēśvara), how can anyone who is not īśvara survive touching other men's wives? Only Gauri's īśvara (husband of Gauri) can drink the dreadful poison and survive.
Clearly, the attempt in these verses is to justify Krishna's transgressions. Whether Krishna is treated as an īśvara (Lord) or a paramēśvara (Supreme Lord), these verses are all about how their apparent sinful actions are unimpeachable.
Almost reminds us of Nixon's quote: "when the president does it, that means it is not illegal." Did Nixon read BhP? :-)
I still believe your attempt to connect īśvaras in these verses with Āḷvārs is far-fetched.