Do you have ANY field experience? If your employer is THAT flexible, maybe do some shift swaps, so you can pull a part time gig as an EMT. Even those nonemergency transfers result in patient contact, and the way you talk to a patient and care for a patient will make you or break you as the paramedic you want to become. I wouldn't want you to be the guy at the station who people think of as a crappy medic. I know some medics who went straight from EMT school to paramedic school back in the 80s, and i can assure you that they weren't golden when they first got the EMS job. The BLS part time gig will either show you, or shove it coldly in your face, how to ask questions in the RIGHT way, giving time for old people to answer, and give you hairy situations to make you think.
Yes, having some prior EMS experience will help you. But you start class in september. You say you work alot. Stop working all the extra hours as the Lab Tech, and pull that extra time over at the Fish & Bone Ambalance Service. Get your 'stupid' questions out of the way as an Part-Timer. Learn/Put to use a myriad of styles of Total Body Lifts, Sheet pulls, and the management of certain scenes they may or may not have covered at EMT School. Get patients who need C-Spine Immob. out of bathtubs. Get used to Ambulance Operations.
You only have a few months, so I would advise to get as much experience as possible. If not for the patient contact, then for the experience with operations and patient care reports.
1 more question: how does your pay as a lab tech fall with the pay of a paramedic in your area?
Evan