Swami,
The exact verse in Srimad Bhagavatham is found in 8th Canto, 2nd chapter 29th verse
niyudhyator evam ibhendra-nakrayor
vikarṣator antarato bahir mithaḥ
samāḥ sahasraṁ vyagaman mahī-pate
saprāṇayoś citram amaṁsatāmarāḥ
And yes it clearly says One Thousand Years. Also, at the beginning of this chapter, Sukadevar described the location of this lake
śrī-śuka uvāca
āsīd girivaro rājaṁs
trikūṭa iti viśrutaḥ
kṣīrodenāvṛtaḥ śrīmān
yojanāyutam ucchritaḥ
Sri Śukadevar said: My dear King, there is a very large mountain called Trikūṭa. It is ten thousand yojanas [hundred thousand miles] high. Being surrounded by the Ocean of Milk, it is very beautifully situated.
So it’s not in this booloka plane but in a higher plane surrounded by an ocean of milk. He also goes further and says in verse 5,
siddha-cāraṇa-gandharvair
vidyādhara-mahoragaiḥ
kinnarair apsarobhiś ca
krīḍadbhir juṣṭa-kandaraḥ
The inhabitants of the higher planets — the Siddhas, Cāraṇas, Gandharvas, Vidyādharas, serpents, Kinnaras and Apsarās — go to that mountain to sport. Thus all the caves of the mountain are full of these denizens of the heavenly planets. So this is a higher planet where souls with longer life term reside.
Even though there is no specific mention of which yuga this incident as per adiyen’s understanding, it should be certainly one earlier than ours, which certainly has a longer life term.
So with this basis, it becomes quite logical for Sukadevar’s statement: “O King, the elephant, and the crocodile fought in this way, pulling one another in and out of the water, for one thousand years.”
Said that, adiyen always remembers Gajendra Moksham in 3 words as mentioned by our Swami quoting Velukkudi Sri. Varathachariar Swami’s words
“வாரணம்-காரணம்-நாரணம்”
Sri Velukkudi Krishnan Swamigal Thiruvadigale Saranam
Adiyen,
Badrinarayan Ramanuja Dasan