GWAS: why is replication in another cohort so crucial?
As an elaboration of my comment.

Summary: Replication is required in GWAS studies to account for non-random technical biases.

An example of such bias is, for example, a chip used for genotyping giving consistently incorrect genotypes for a locus. In this situation adding more subjects will not correct for this effect and therefore the only solution is to genotype additional subjects with another method (e.g. another chip or experimental protocol). Another source of non-random technical bias is at the phenotype measurement level. You might want, if possible, to measure the phenotype using other techniques to make sure that bias will be corrected.

A replication cohort does not need to be huge and the actual size needed will largely depend on the effect size of the SNP seen in the discovery cohort. A "power-to-detect" calculation would help in predicting the cohort size needed. For a SNP to be significant, it must pass Bonferroni correction but as you can run a statistical test at the candidate site only the correction will be usually not very astringent (i.e. you might run association tests on "only" a few dozens or hundreds SNPs).

Historically GWAS replication was also required to correct for population structure but as the tools evolved substantially (e.g. the use of principal component analysis) and the cohort sizes are now substantially bigger compared to the first GWA-studies, this is less a concern. What was required is to sample independently other subjects from either the same or a different population.

For your situation what you could do is to split your cohort into a discovery and a replication panel, genotype your subject in the replication panel using an independent technique, eventually do the same with the phenotyping and replicate you candidate SNPs. The replication panel needed is usually must smaller than the discovery cohort for the reasons stated in the previous paragraph.

For your last question about the meta-analysis. Yes this could also be a way to go but be careful that you will still need a replication cohort to validate SNPs found this way therefore resulting in the exact same problematic you described. 

I hope this help!