Hey, this sounds like a very interesting problem :)

Statistics not being my strong topic, I would go for a very straightforward approach.

Taking your proposed genome size of 3Mb and the 10000 homozygous SNPs into account, I would calculate first the expected average SNP density over this genome (not really realistic, but it's a start). 3Mbp/10k = 300bp

This would mean you would on average expect to encounter a SNP in your genome every 300 bp.

Now I would consider your genes that contain the 400 SNPs and calculate their (length divided with the expected SNP density) and exclude those that have this value higher than the actual number of SNPs. For example a 400bp gene with 1 snp would be excluded but a 500bp gene with 2 snps would be included. In this way you would get a set of genes that have a higher than average genomic snp density or "snp-enriched genes". Then I would use them as the subset list_2 in your enrichment analysis.

If you wanted to take into account local snp hot-spots and differing variant distributions throughout the genome, then you would need to fit a model to the data and test enrichment according to that model to get "snp-enriched genes" for your specific genome.

If you have a number of SNPs that you expect to see per gene, then you can calculate the z-score and use a cutoff to decide whether a gene is over- or underrepresented for SNPs.

I believe the first thing to do is to actually filter the list SNPs, leaving only those that are in coding region and are non-synonymous ones. This would automatically remove the bias for gene length, as it mostly comes from introns. Then I would actually go for the standard testing (gene ontology).

If a more detailed view is needed, I think the best way to do is to look at protein domains affected by non-synonymous SNPs and do an GO enrichment test for them.

Of note, usually the problem is quite inverse - sparse sets of genes are affected by mutations, and the functional enrichment of interest usually reveals itself when those sets are somehow "smoothed", see this paper for example.

From the other point of view, one could be interested in analyzing the synonymous/non-synonymous substitutions and polymorphisms (see McDonald-Kreitman test), to see which genes are under genes are under positive/negative selection and perform functional enrichment tests for them.