You are absolutely right. I should have been clearer. In Mahanidana Sutta, Buddha starts the exposition from consciousness and Avijja and Sanskara are omitted.
"“It was said: ‘With consciousness as condition there is mentality-materiality.’
How that is so, Ānanda, should be understood in this way: If consciousness were not to descend into the mother’s womb, would mentality-materiality take shape in the womb?”
“Certainly not, venerable sir.”
“If, after descending into the womb, consciousness were to depart, would mentality-materiality be generated into this present state of being?”
“Certainly not, venerable sir.”
“If the consciousness of a young boy or girl were to be cut off, would mentality-materiality grow up, develop, and reach maturity?”
“Certainly not, venerable sir.”
“Therefore, Ānanda, this is the cause, source, origin, and condition for mentality-materiality, namely, consciousness.
“It was said: ‘With mentality-materiality as condition there is consciousness.’ How that is so, Ānanda, should be understood in this way: If consciousness were not to gain a footing in mentality-materiality, would an origination of the mass of suffering—of future birth, aging, and death—be discerned?”
“Certainly not, venerable sir.”
“Therefore, Ānanda, this is the cause, source, origin, and condition for consciousness, namely, mentality-materiality.
“It is to this extent, Ānanda, that one can be born, age, and die, pass away and re-arise, to this extent that there is a pathway for designation, to this extent that there is a pathway for language, to this extent that there is a pathway for description, to this extent that there is a sphere for wisdom, to this extent that the round turns for describing this state of being, that is, when there is mentality-materiality together with consciousness"
From the above it should be clear that name & form and consciousness are interdependent and descending consciousness even though it is called relinking since it has a sort of father to son connection it is one of the six types. Here Buddha says “descending” not to indicate that consciousness is equivalent to birth as the 3 life interpretation takes it but to emphasize the dependency of name & form on consciousness and consciousness on name & form.