Another treatment I've seen used is one of the spray paints formulated for plastic, such as Krylon Fusion. If you find a color that matches what you want, it's just a matter of masking EVERYTHING and you can treat the endcaps in place.
I've heard that results on tambour are iffy, because the action of the tambour scrapes paint, so that might be an issue if you have tambour the same color as the end-cap (like on my '75 Argosy) but if you have dark woodgrain tambour that you mask off or remove when you're treating the rest, it seems like it could work.
Zero Gravitas — 2017 Flying Cloud 26U | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill