Very easy to test for carotenes at home with commonly available materials.
Extract the pigments with a solvent.
Run a paper chromatography test.
If you keep the concentrations of your tests consistent, you would be able to dry the test strips, and compare them one against another to determine which has the highest concentration of carotenes.
You could even make it semi-quantitative by using β-carotene vitamin pills to make control solutions of known concentration.
For example:
http://www.hsu.edu/pictures.aspx?id=1653 will give you ideas about what keywords to search for additional details. "Paper chromatography carotenoids" is a great search term.