Is every “even” polyomino with one hole tileable by dominoes?

In Conformal Invariance of Domino Tiling the author defines an even polyomino as a polyomino with all corners "black" if the polyomino is colored with the cehckerboard coloring. A corner is black if it is one of these types:
Here are two examples:
My question is whether it is true that an even polyomino with one hole is always tileable by dominoes.
Background: A related polyomino is called a Temperleyan polyomino (in the same paper), which is formed from an even polyomino by removing one black corner from the outer border, and appending a black cell to each interior border. Here are some examples:
The paper shows (although not really in a way I can follow) Temperleyan dominoes are tileable by dominoes.
It is also easy to show that the deficiency (black minus white cells) in an even polyomino with
H
H
holes is
1−H
1
, so a even polyomino with 1 hole is balanced (has the same number of black and white cells).
The holes of even polyominoes are also even.

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