Rupa Goswami quotes in Laghu Bhagavatamrita in 4th section from Padma Purana.
äviñöo’bhüt kumäreñu närade ca harir vibhuù ||36||
yathä tatraiva --
äviveça påthuà devaù çaìkhé cakré caturbhujaù ||37||
äviñöo bhärgave cäbhüd iti tatraiva kértitam ||38||
etat te kathitaà devi jämadagner mahätmanaù |
çaktyäveçävatärasya caritaà çärìgiëaù prabhoù ||39|| iti |
"All-powerful Lord Hari entered the Kumaras and Narada "
In the same book:
"The Supreme Personality of Godhead, who has four arms and holds a
conchshell and cakra, entered Maharaja Prthu."
In that book it is also said: "The Supreme Personality of Godhead also entered Parasurama."
It is also said:
"0 goddess, I have thus described to you the pastimes of Lord Parasurama, who
is a sakty-avesa-avatara of Lord Visnu."
I don't know any thing about the previous birth of Lord Prasurama.
Pre Gaudiya commentator on bhagavata, Sridhar swami also uses such classification.
In his commentary on 1.3.28
kumära-näradädiñv ädhikärikeñu yathopayogam aàça-kaläveçaù | tatra kumärädiñu jïänäveçaù | påthvädiñu çakty-äveçaù |
Padma Purana, Uttarakhanda, Chapter 241 has details of Parasurama. Lord Siva relates the story of Parasurama to mother Parvati.
This chapter describes Parsurama is born by benediction of Indra. Parasurama is a jiva. Later in life, he worshiped Vishnu and then he became sakty avesa avatar.
Few of the verses:
Kasyapa gives Parsurama some Vishnu mantra..
17-?. Having received the formula from Kasyapa, the high souled one,
(Parasu-)Rama, muttering day and night the great six-syllabled
formula, worshipped the lord of Laksmi. That pious Bhargava (i.e.
Parasurama) meditating upon Visnu having eyes like lotus-petals and
the omniscient one, practised penance for many years...
Pleased by his worship
God Visnu said: 40-41. O child,
with the penance of you of a controlled mind, I am pleased. O
brahmana, I shall give you a very auspicious power. Possessed of my
power, kill the wicked great kings for destroying those who cause a
burden to the earth and for the good of the deities.
79-81. O goddess, I have told you this account of the incarnation of
lord (Visnu), holder of the Sarnga bow, who had entered Rama with his
power. Due to the entrance of the power this (form) of the noble one
cannot be worshiped. The chief, noble, brahmanas, the devotees of the
lord, should worship the incarnations of (Dasarathi) Rama and Krsna,
perfect with virtues, worshiped by sages, and giving salvation to