Other than dropping a flight medic packet is there any other way a normal 68w can attend paramedic school through the Army?

Get assigned to the 83rd Civil Affairs Bn at Bragg, that'll be your first stop after inprocessing. Or you can go beyond a Paramedic and go to SOCM via 18D, 38B, Ranger medic, 160th Medic, or get lucky and get some other random ARSOF assignment as a medic.

The Armys paredic program is a part of the flight medic pipeline, the Army isn't going to pay to send people to paramedic if it doesn't support a specific mission requirement. Some posts have worked out programs with their local paramedic programs to send their medics locally.

So the question is whether you want to attend an Army paramedic course or if you are trying to get a credentialed EMT certification for post military life. Military schools have to have a cause,effect and relation to what they are doing to be justified as you are dealing with high level school funding.

With that said the local unit level has some flexibility there. When I was in the Marine Corps you would occasionally see the Unit Corpsman work some magic with local trainers and host EMT courses for Marines/Sailors to attend to get certified. I emphasize the word occasionally because it wasn't an annual event and not something you could always depend on. It was case by case and when funding/time allowed. But for those who were lucky they got some primo training by a combo training staff of Military Medics and active EMT's. Wealth of knowledge out of the wazoo. But it wasn't traditional training pipeline stuff.