Earlier today I emailed a friend with some negotiation advice. I thought some of you might find it helpful, so I've decided to share those tips here. For more tips, refer to Five Minutes to a Higher Salary.
Put all your asks at once.
If I'm reading it correctly, it sounds you've put out your base salary request, but not your title change request.
I'd put in an email ASAP and say,
"One more thing I forgot to mention, I'd like to have a title of X instead of Y because ...."
Last thing the hiring manager wants is a protracted negotiation or the feeling that you're stringing them along.
Explain your reasoning.
I'd prefer the title X because...
(Your explanation sounded reasonable to me: entry-level, limits future prospects because it sounds niche, etc.)
Prioritize, if asked.
It's absolutely okay to ask for multiple things (salary and title change). You might get both!
However, if they ask which one is important to you, do be clear on which one is more important. Not stating can come across as being difficult, unreasonable, greedy, etc.
I can't imagine you not being nice. :)
I know you don't want to lose this offer, and just a reminder that offers *only* get lost when candidates take the offer personally (aka low offer = reflection of self-worth), get emotional (e.g. "you make me go through this crazy job process and you insult me with this") or tries to copy actors in TV shows (e.g. "this is my final offer" -- i.e. no ultimatums).
Photo credit: Strelka Institute for Media, Architecture and Design