Let´s just calculate the doubling window with the assuption that Black redoubles immediately, because he can´t win much by keeping it:

White´s doubling point: 3.8% : (3.8%+1.5%) x 100% = ca. 72%.

Black´s takepoint: 1.5%: 7.8% x 100% = about 19%.

White´s doubling window (72%-81%) is higher than in a money game because of the lead in the match, but it is not so high that the leader has almost no opportunity to double. Positions where the leader and the trailer can win almost no gammons are easy to handle: The leader should double if his winning chances are near to 80% and the trailer should take if he has up to about 19% winning chances.

But if there are gammons involved, the leader has to reflect whether he wants to count the gammon wins or whether he allows the opponent to double out his gammon wins by redoubling and to make the trailer´s gammon wins more effective. In these circumstances a trailer´s gammon win more than doubles his match equity (20:11 => 20:15).

Here is the calculation of White´s doubling window considering gammons as an example:

White (the leader) wins about 25% of the games he wins gammon and 1% backgammon (as in the problem position).
Black wins about 20% of the games he wins gammon and no games backgammon.

White´s doubling point: (95.8%-90.1%):(95.8%-90.1%+100%-98.7%)x100%= 5.7%:(5.7%+1.3%)x100% = 81%.

Black´s takepoint: 1.5%:9.9%x100%= about 15%.

Considering gammons White´s doubling window narrows (85%-81%).
In the problem position Black has at least a deuce-point game and therefore he has more than the winning chances demanded by the doubling window.

Correct cube action: No double - take/redouble.

White doesn´t win many ganmons any more and also seldom loses one.

However, Black has almost 20% winning chances with his badly timed deuce-point game because White´s 5-point is open.

From the calculation in the last problem position we get the correct cube action: Double - take/redouble.

When should the trailer double being so far behind in the match?

Again let´s calculate the doubling window considering gammons and backgammons first.

Black wins about 30% of the games he wins gammon and 2% backgammon.
White wins about 30% of the games he wins gammon and 1% backgammon.

Black´s doubling point: 0.5% : (0.5% + 0.8%) x 100%= 38%.

Takepoint für Weiß: 1% : 3%x100%= 33%.

Black can expect a correct double in between 38% and 67% winning chances!

In the problem position Black is a clear favorite to win the game and the position is very volatile.
A hit may easily raise Black´s winning chances over 70%, because if White´s blitz material decreases, his winning chances decrease quickly at the same time.
Therefore Black has to double now. Black doubles out the additional value of White´s gammon wins and increases the value of his own gammon wins. With slightly more than 40% winning chances White has a clear take.

Correct cube action: Double - take.