I've not seen a tulip that color. Duh, Calf. here. But have you seen Princess Irene? The orange / red stripes might work.

Princess Irene was my first thought as well :-) A combination of orange, red and purple, it combines beautifully with red leaved trees and shrubs.

Be sure and avoid as many of the maple roots as possible. JM's are very sensitive to root disturbance and you can easily damage them or spread/encourage diseases by anything more than minimal disturbance.

The species are probably your best bet - such as hageri, whitallii, orphanidea and even sprengeri. Although, my recollection is of maple leaves appearing quite some time after the last tulips bloom (but this is in my UK climate). I think only sprengeri, which is the last tulip to bloom, might coincide. There is also a lily-flowered tulip called 'Burgundy' worth searching for...and a whole slew of orangey coloured, feathered Triumphs such as Dillenburg, Burnt Sugar and Cairo.

I think in your zone tulips and Japanese maples would meet up. Friends of ours have Gavota under a Japanese maple. Burgundy and yellow. Not as striking as an orange blend, but very harmonious, with the yellow giving it zip.

Or any of those Queen of Night, Ronaldo, Havran, Black Jack 'black' tulips..and I am certain there are a few double lates such as Uncle Tom..