Should you negotiate salary on an internal move?

Hey everyone. I'm finishing up a 2-year high-potential rotational program I started with my company after graduating in 2014 (engineer) and they really want to hire me on where I'm currently spending my last rotation. I applied and made a verbal commitment, and they sent me an offer last week. My question is--is it appropriate to make a counter-offer when I'm an internal candidate for the job posting?

I currently make 70k and they're offering me 76.5k (~10% more). Based on my knowledge of the salary bands, my coworkers in the same position (with 10-25 years of experience) all make around 105k-135k. Obviously, if I stay here, promotions will take me there, but for now, I feel like this is the crucial point in my career to set my salary base, so I think I definitely want to negotiate. I don't know if this is taboo internally or what. I figure the worst that can happen is they say no. I think I have some leverage:

• I've been working in that exact position for a year with nothing but great feedback to my manager (can also pull out my stellar performance reviews and list my accomplishments)
• I was in this "high potential" program, so I can reference the salaries of other people in this program who made more
• my manager is on my side and likes me a lot
• I'm the only person under the age of 35 and they really need younger people
• the position requires 8+ years of experience, so they dropped the salary band to my level and can pay me less, but I'll still be doing that higher-level work, and I can point that out
• I can also point out that hiring internally is cheaper than hiring externally
• I have a copy of the salary bands, and they offered me smack dab in the middle of that salary band... so I know there's wiggle room

Do you think this is a good idea? Should I respond to the offer letter email with a well-written response, or set up a conference call with the recruiter?