Your situation reminds me a lot of my own (I know exactly what version of "Amazing Grace you’re referring to), except that there is a TLM parish within manageable walking distance of my house (I can’t drive, either).
If you want to convince your pastor to start a TLM at your own parish, you will need what others have mentioned: a group of interested (if not committed) people in your parish. If you can find a group of people who want it, you or the member of the group whose contributions make up the highest percentage of the weekly collection should approach the pastor in a non-confrontational manner and ask if he would be willing to explore the possibility. If you can’t find a good-sized group, you could always mooch a ride to a Latin Mass (or at least a more reverent one) from a like-minded parishioner with a driver’s license.
When my parish first started heading in the direction of your current parish, a number of the more traditional parishioners left and found more reverent Masses. If you had any way of contacting them, they might be willing to help, too.
Unfortunately, the most important thing you need is a receptive priest. If your pastor doesn’t like the idea, there is little you can do in your current parish to get a TLM. You could still try to let him know that some of the song selections and certain other aspects of the Mass make you feel uncomfortable, but remember to never call a man’s baby ugly. Much of what is happening at your parish might be part of a deliberate effort to make the Mass more accessible. The worst thing you could do is approach your pastor with self-righteous indignation, waving Summorum Pontificum in his face. If you respect his intentions and the efforts of the laypeople who bothered to volunteer their time to help plan the liturgies, he’ll be more likely to respect your concerns.