What advice do have on being taken more seriously as an E-4 senior medic within a battalion where senior medics are E-6?

My best advice is to study and learn everything you can. When it comes to the medical field your knowledge and competence is what sets you apart.

Pretty sure Senior medics are an E5 slot, or at least it was when I was an E4 Senior medic.
The best way to be taken seriously is to know your craft inside and out as if you are a higher rank. Speak with the confidence of someone who knows what they're talking about and people will listen. If you don't have it already, start expanding your skill set with EMT-I, EMT-P, EMT-I, PHTLS, ACLS, PALS, etc.

Act more seriously. IF you are the senior medic be the senior medic. Soon enough...in the bigger picture...if you are the senior medic your rank will come in line.

The short answer is to be capable and execute your mission. Your capability as a medic has little to do with the rank you wear. Your demonstrated capabilities will be what makes people take you seriously. Keep your motivation high, but don't confuse enthusiasm with capability. Seek every opportunity to train your junior medics. Work with your leadership to integrate casualties into every drill and exercise. Assign homework and self-study. Make sure your medics are squared away in their personal and professional lives through solid counseling. And while you are leading and developing others, you must also develop yourself. As the senior medic, you may not have the kind of direct mentorship you'd want. Seek out senior medics in other organizations and ask them for advice. Take time to pursue education when you can. I recommend starting some of the medical courses on ALMS such as the SOCM Prep Course and the 18D Prep Course (you can sign up through the ATRRS Self-Development Center). Once the ECM program launches, put in your packet as soon as you can. In the meanwhile, live your NCO creed and remember that the mission comes first, then your Soldiers, then your own needs.

Be the subject matter expert.

Just do you job well and give sound advice. Those who need your care will recognize your abilities and treat you in accordance to how you present yourself. If you appear confident and competent, you will quickly garner the respect you earn for yourself. Being a good medic isn't just about knowledge, it's about knowing people, knowing when something is wrong beyond the obvious and knowing how to fix problems or where and when to send those with problems for further care. Normally I would expect at some point a recommendation for CPL Stripes, though some commands are less inclined than others to issue those stripes. SGT will come soon enough, just work on getting correspondence course done and take some college courses if you can. Distinguish yourself from your peers. All of these things will earn you respect and cause you to be taken more seriously.

Learn as much as you can from your provider. So that you will be the best resource for your Command to come to you when there is a medical issue. This is not just a Band-Aid but readiness, and issues with malingering and profile rangers. Not that they haven't been doing this for a few days but those issues do come up. Education wise start working on Paramedic if that is your goal or nursing, RN. Those areas will also give you a leg up.

Be professional and know your stuff. If you don't know, don't pretend that you do.

I was in that same boat and I have a buddy who joined who had years of experience. Sometimes they just do not see you for anything but your rank. Continue to learn and expand your skills and don't back down.

Yep, get promoted to E-6, or even E-7. ;-)