You need to be very clear what you are trying to accomplish. If this is about trying to get more development work done with the same number of staff, changing titles won't do the trick. To do that, you need to reduce the operations work and/or increase the development productivity.
I would avoid restructuring or changing roles at this point. I would instead make changes around reducing operations work and increasing development productivity.
May I suggest ...
1- Measure where time is going. There are typically three "flavors" of work in this kind of environment: urgent support, minor development (i.e. small enhancements), and pure development. You need to know how much time is being spent on these. Do not trust your own estimates .. they are probably way off.
2- Designate a primary support role, and have that role rotate among the staff. The current "primary" is tasked to catch support issues and deal with them, leaving the rest of the staff free to work on projects. The idea is to give the staff more uninterrupted time for development, which should help productivity.
3- Implement a ticketing (i.e. issue tracking) system if you don't already have one. Press users and your team into using it, and make the team keep it updated.
4- Be open and clear with the groups you are support about what you are doing and why you are doing it. Push back on them about needless requests things and overblown urgency.
Once you have more data and have made some changes, then you can make better decisions about "structural" changes. If you do decide to split your team, you will likely have more data about which person belongs on which side of the wall.