Assemble reads for a specific gene
That's a good question. I remember seeing a poster about making trees directly from reads, but unfortunately, I can not find any other record than this tweet. Perhaps you can try to email David, if he would be keen to share the implementation. 

While searching for any information about David's work, I run into a GitHub repository called reads2trees. It's quite old and it's not super popular, so hard to say if it can be useful. But the name matches the problem description quite well.

I also remember there were some attempts (An example paper) to get phylogeny directly from kmers, but I have never tried that on my own. I also think these approached were focused on microbial phylogienies. So again, not sure if it's going to be useful for you.

That's all I got.