Are there avenues/options to pursue a medical degree (with funding) after a Ph.D.? I have a Ph.D. in Engineering and I figure a medical degree will be highly valuable to gain a better understanding in my research area (biomedical/neuroscience). However, unlike science/engineering graduate schools, medical schools do not pay your tuition and financial assistance is primarily need based, rather than merit based.

Are there avenues for an interested candidate to pursue a medical degree in the US (perhaps part-time, while working as a post-doc in a relevant field) without taking on significant amounts of debt?
Speaking as a graduate of an MD/PhD program:  

You will not learn what you seek in medical school. 


Medical school is largely worthless unless you pursue residency. Very little basic science is taught in medical school. The education is closer to word association that builds the foundation for the pattern recognition that is diagnosis. I found nearly no overlap between my medical school training and graduate training (PhD in electrophysiology, lots of electrical engineering, software development, and surgery on large and small animals). The most notable overlap was that I knew how to tie sutures for my surgery rotation.  
If you pursue residency, most academic places will require you to practice medicine and do research. There are only 24 hours in the day. Seeing patients brings in more money more reliably than most research. A background in engineering suggests a surgical subspecialty. There is a reason most neurosurgeons and orthopedic surgeons consult or participate in a research group rather than run it. 
Medical school is a full-time job. It is not like law school where you can attend night classes. 
Attending physicians will not have an equal conversation with medical students Medicine is hierarchical. If you mark yourself as a student, you may find it difficult to have substantive scientific conversations with those above you in the medical ladder until you finish residency (at best 10 years after you start).