It is not likely that you will find a lot of flexibility at the schools you are considering. Faculty usually need to have students really working full time on their research if it is funded and they need to deliver results. The is particularly true in engineering and the hard sciences. If you do find someone who is willing to supervise you in a part-time setting, it will probably not be the top faculty member in the department.
In order to do this, you need to convince a faculty member to take you on and support your application to the program.