Logo Color Modification for Screen Printing

I urgently need an existing logo color edited for visibility on a black case. The current design contains black lines which will be invisible when screen printed on a hard black case.

Key Requirements:
- Retain only the red color in the logo
- Modify the black
- Suggestions for a professional and clean color scheme

I am leaning towards changing the black to white while keeping the red intact. However, I am open to your expertise and would appreciate seeing options that include shades of gray.

Deliverables:
- Edited logo in .ai, .png and .jpg or .jpeg formats

Ideal Skills:
- Graphic Design
- Logo Design
- Adobe Illustrator Proficiency

Please ensure the final design stands out when silk screened on the black hard case. Thank you!