Metamagic rods don’t raise any “effective level” – they explicitly don’t change the spell’s level at all. Yes, you can use a metamagic rod on a spell even if the change made by the corresponding metamagic feat would increase the spell’s level above 9th. Since the rod is explicitly not doing that, it doesn’t matter that the feat would (and the description of the rods make no mention of a special restriction along those lines).
Note that the greater echoing metamagic rod is kind of wasted on your 6th-level spell cast from a 9th-level spell slot, since a regular echoing metamagic rod would work on that. But no, it does not affect anything.