I like #6 and 7. Thats a good simple strategy instead of trying to figure out which tickets get automatically pushed to sr engineers! I can only see it working if you have the man power to keep up with the tickets.
Currently my team is a disaster. There is only me and one other person with IT backgrounds and the rest have just been pushed into their roles. Over the past 5 years our department has slowly transitioned into an IT style team but no one besides me and the other IT guy can see this. Leadership is 100% project management focused and does not know how to run an IT team. Hell both supervisors dont even know the first thing about networking or system administration. They quickly get confused between RAM and Hard drives

I quickly lead on to this and thought it would be a great opportunity for me to steer the team onto a good track but all I get is resistance. "We are not your typical Enterprise network, so best practices don't apply" , "We dont have time to implement your suggestions, just focus on the projects". This also has lead to everyone on our team going in their own direction with little to no cordination between each other on projects. I can go on for quite a while on this...
Mentoring is a huge part of me. I love to teach others and help them grow (if they want too). We hired a new girl about 4 months ago straight out of desktop support with no server or networking experience. I was hoping my boss and her co-workers would setup a mentoring program with her or at least give her direction... Nope, nothing. Just here are your projects and get to them.
And yes, we are a team of 15 and there is only 3-4 of us who do everything. When someone elses system breaks they dont know how to TS or fix it, freak out then pull one of us in to save the day.
I miss a normal IT team...