it's probably not worn too much, the chain may skip a little bit until it beds in. No two chains are ever exactly the same, it will take a few miles to settle the new chain in.
"it's probably not worn too much" - I agree. 6000 miles is small beer for a chainring. Significant wear is rather unlikely. 15,000 maybe.
"the chain may skip a little bit until it beds in." What is this 'bedding in' thing? Is the chain 'stretching'? Is the cassette suddenly 'wearing'? If a new chain skates on a new cassette there's something amiss.
"No two chains are ever exactly the same" Chains for the same speed are the 'same' enough to mean that any actual difference is minute (in the context of chain skating).
The new chain has got factory lubrication on it which should do through to the first Mickle.
Guess again.
Like you, rr, I think the OP needs to look elsewhere for the cause.