Is this step justified?
I'm a little confused what OP's argument is. If you say "it should be a meta attack for methoxide group," then the question is showing an electrophilic substitution at meta-position to methoxy group. But, I understand you are wondering why substitution is at the meta-position to methoxy group rather than on ortho-position to methyl group. If that's what you meant, this is the answer to your curiosity:

The step in question is an example of Friedel-Crafts reaction. More precisely Friedel-Crafts acylation reaction. Here though, the substrate (aromatic nucleus) and the reagent (acyl chloride) are in the same molecule unlike any other typical inter-molecular reactions. In any inter-molecular Friedel-Crafts reaction involving 4-alkylanisole, substitution of acyl group mainly occurs on ortho-position to methoxy group, as you pointed out that "an oxygen atom's conjugation would be more contributing than carbon's hyperconjugation and inductive effects combined." I said here mainly because there would be some minor product from the substitution at ortho-position to alkyl group as well. For example, according to my experience, when Friedel-Crafts acylation reaction is performed in toluene and chlorobenzene, there were mixtures of products including o- and p-chloroacylbenzenes.

Now, we look at the problem in hand. This reaction come down to inter- versus intra-molecular acylation reactions. It's always intra-molecular reaction is much more faster than same type of inter-molecular reactions (here is acylation reaction of both kind) due to proximity. Thus, this phenomenon overcomes the deficiency of activation by methyl group versus methoxy group here, and gives most thermodynamically stable product, 7-methoxytetralone as the major product.



Edit: As OP's request, I include here an example for intra- vs inter-molecular acylation reaction (Ref.1):





Reference:


Yingju Xu, Mark McLaughlin, Cheng-yi Chen, Robert A. Reamer, Peter G. Dormer, Ian W. Davies, "A General Method for the Synthesis of 3,5-Diarylcyclopentenones via Friedel−Crafts Acylation of Vinyl Chlorides," J. Org. Chem. 2009, 74(14), 5100-5103 (https://doi.org/10.1021/jo900696k).