Speaking as someone who has been the one hiring devs for about 8 years now, I think you need to take a bit of control of the hiring / interview process, because you're not going to make many inroads if you go by their playbook. Companies are getting wary of front end developers without much professional experience since there tends to be a pretty massive talent differential, and no real easy way to judge who's capable.
Find a way to speak directly to someone in engineering - preferably someone who is doing the hiring. If you can meet someone in person at a meetup that's best, but e-mail works otherwise. Offer to do a project for them to demonstrate your skills. Almost every company is going to have something that's not on the critical path that they could use help with. You should get paid for this - try to figure out what freelancers make in your market and price within it, but on the low end (don't try to undercut the entire market).
Find a way to speak directly to someone in engineering - preferably someone who is doing the hiring. If you can meet someone in person at a meetup that's best, but e-mail works otherwise. Offer to do a project for them to demonstrate your skills. Almost every company is going to have something that's not on the critical path that they could use help with. You should get paid for this - try to figure out what freelancers make in your market and price within it, but on the low end (don't try to undercut the entire market).