I quote my previous statement:
"Roman rule never officially ended in Spain save for the transition of power to the Visigoths."
A first step would be to show how the Roman governorships in Iberia were transferred to the Visigoths.
As already noted, the last Roman governing authority in Iberia was granted by Honorius to his half-sister Galla Placidia. She married Athaulf, the Visigothic king, and allowed his people to settle in Iberia. Athaulf was assassinated in Barcelona in 415. His throne briefly seized by the assassins, but the Visigothic succession was quickly restored under Wallia. Wallia became a close ally of Roman Emporer Honorius and was recognized by treaty as a Foederatus of the empire with settling rights in Iberia, thus completing the cession as Rome withdrew. As Gibbon describes it:
"A solemn treaty was stipulated and observed; Placidia was honorably restored to her brother; six hundred thousand measures of wheat were delivered to the hungry Goths; and Wallia engaged to draw his sword in the service of the empire. A bloody war was instantly excited among the Barbarians of Spain; and the contending princes are said to have addressed their letters, their ambassadors, and their hostages, to the throne of the Western emperor, exhorting him to remain a tranquil spectator of their contest; the events of which must be favorable to the Romans, by the mutual slaughter of their common enemies. The Spanish war was obstinately supported, during three campaigns, with desperate valor, and various success; and the martial achievements of Wallia diffused through the empire the superior renown of the Gothic hero. He exterminated the Silingi, who had irretrievably ruined the elegant plenty of the province of Btica. He slew, in battle, the king of the Alani; and the remains of those Scythian wanderers, who escaped from the field, instead of choosing a new leader, humbly sought a refuge under the standard of the Vandals, with whom they were ever afterwards confounded. The Vandals themselves, and the Suevi, yielded to the efforts of the invincible Goths. The promiscuous multitude of Barbarians, whose retreat had been intercepted, were driven into the mountains of Gallicia; where they still continued, in a narrow compass and on a barren soil, to exercise their domestic and implacable hostilities. In the pride of victory, Wallia was faithful to his engagements: he restored his Spanish conquests to the obedience of Honorius; and the tyranny of the Imperial officers soon reduced an oppressed people to regret the time of their Barbarian servitude."
A second step would be to demonstrate how and when these appointed positions became hereditary.
Through the hereditary line of the Visigothic kingdom. The line continued through Roderic, who was slain by the mahometan invaders in 711. The line eventually passed to Pelagius of Asturias, the highest nobleman to survive, whose reign founded most of the dynasties that became parts of the Spanish crown today.
So Roman rule ended with the transition of power to the Visigoths. Thanks for clearing that up.
Wallia became a close ally of Roman Emporer Honorius and was recognized by treaty as a Foederatus of the empire with settling rights in Iberia, thus completing the cession as Rome withdrew.
In other words, Visigothic Iberia was an ally of Rome but had a very different legal and administrative system and was recognized both by its own rulers and those of Rome to be a new state on the peninsula.
Through the hereditary line of the Visigothic kingdom.
Which is another break with the Roman administration of the province. Furthermore, Honorius's grant to Galla Placida could not pass through hereditary succession because neither she nor her husband left any heirs. As Gibbon describes it:
The fondness of Adolphus for his Roman bride, was not abated by time or possession: and the birth of a son, surnamed, from his illustrious grandsire, Theodosius, appeared to fix him forever in the interest of the republic. The loss of that infant, whose remains were deposited in a silver coffin in one of the churches near Barcelona, afflicted his parents; but the grief of the Gothic king was suspended by the labors of the field; and the course of his victories was soon interrupted by domestic treason. He had imprudently received into his service one of the followers of Sarus; a Barbarian of a daring spirit, but of a diminutive stature; whose secret desire of revenging the death of his beloved patron was continually irritated by the sarcasms of his insolent master. Adolphus was assassinated in the palace of Barcelona; the laws of the succession were violated by a tumultuous faction; and a stranger to the royal race, Singeric, the brother of Sarus himself, was seated on the Gothic throne. The first act of his reign was the inhuman murder of the six children of Adolphus, the issue of a former marriage, whom he tore, without pity, from the feeble arms of a venerable bishop.
The line eventually passed to Pelagius of Asturias, the highest nobleman to survive,
Since you have proven eager to hide unpleasant facts in vagaries, you will have to prove the legitimacy of Pelayo's claim.