I will suggest you at least accumulate some research experience. Part-time sounds not enough. Research experience is important especially for top programs. The best way is applying for a technician or post-undergraduate intern position and stay for one or two years. That would be much helpful. Also, I think your research experience is not necessary related to neuroscience. Any bio-related fields should be fine. Just show them you can handle experiments and are a quick-learner.
Also I am curious, why you have a thesis in undergraduate but only little research experience? Your thesis is not related to research?
