I don't think there is any significance in the order. However ... however, if I were to prescribe order to the level of intimacy the forefathers had with their Creator, it would be in the following order (among others).
Solomon was a near good for nothing. Possessing great wisdom and yet the fall of Israel was due to his lack of understanding of the whole framework of Creation, the reason for the existence of Israel. He failed to establish a framework of governmentation that would perpetuate the framework for the endurance of Israel.
Perhaps, Solomon had realised that his existence was in vain, but merely being a place-holder. He had absolute faith in his science and near zero faith in his relationship with the LORD. He prayed the typical prayer of preaching to the choir. I doubt his sincerity in that prayer.
Abraham was a schizophrenic fanatic. His faith was tainted by the idolistic legacy of his dad. The LORD tells him one message and he concocts extra messages out of that message. He was told to bring his son to the sacrifice, not bring his son to be sacrificed. Typical fanatics of "going the extra mile". He was supposed to elevate his son and bind him closer. He did not understand the meaning of Qurvan. The language of the LORD was deliberately ambiguous and it was up to him to interpret and he failed the test. Instead of elevating his son, he depressed Isaac, instead of binding him closer he alienated Isaac from him and the LORD.
However, Abraham exhibited as a natural leader. He devoted himself to total faith in his Creator. He was compassionate but his gung-ho fanaticism irresponsibly destroyed the whole of Isaac's character. Isaac became motivationally and emotionally unstable who did not achieve much or at all in his life time.
David was chosen as the administrator to wind down an unnecessary kingship. A kingship with which both Samuel and the LORD were disappointed. Disappointed that the people had chosen to have a king, an anointed phalic messiah, "just like the other nations". That disappointment is reflected in 1Samuel 8.
He tried somewhat to protect his dynasty but without much motivation. His disillusionment led him into various immoral excursions. His intimacy with the LORD led him to understand the anti-climactic role he needed to play. That Israel was not meant to be a kingdom nor be led by a king or messianic hero.
The model of the Divine and Eternal
kingdom governmentation was demonstrated thro Moses and Israel traveling thro the desert. It was not a perfect implementation of the model. Moses seems like a nationalist and a people's person and like getting his hands wet with the issues of the people. However his lack of intimacy with the LORD was demonstrated that Jethro had to give him a few pointers on how to set up a representative democracy. Moses was the right person at the right place at the right time for the right job of delivering Israel out of Egypt.
Also, Moses refused to see his almighty Creator because he was afraid to die. He preferred to see just a shadow of the Almighty. Due to his lack of faith, he could not enter into the Promised Land. Not to mention striking a rock twice.
I would like to skip Elijah and Samuel and go straight to Jacob.
Jacob longed for intimacy with the LORD, as a deer longs for the streams of water. Imagine being in the shoes of the LORD, and Jacob lies and cheats his brother just to be intimate with the LORD, to claim a birth right he did not legally have. Choosing a birthright that would exile him from his material inheritance. He understood the implications and responsibility of that birthright, which Esav disdained.
Imagine the IRS bringing someone to court for fraud in his tax returns and when asked why he/she presented fraudulent information, it was revealed that the reason was he/she wanted to pay more taxes.
Unlike the cowardly Moses, Jacob demanded to see the LORD. Not only see but even wrestled with the LORD. And negotiated with Him just like Abraham did.
Unless a kernel of wheat falls to the ground and die, no fruit would result. Jacob understood what Moses did not - see the LORD to die and be born again in a new enlightenment. Some people go for pot or coke but Jacob went for the LORD.
The enlightenment represents the precision of faith - do not walk that extra mile but walk just precisely enough. The way to life is a narrow and winding path but a broadway leads to destruction. In quality engineering, we ensure a nut and its bolt fit just precisely - we cannot make one an extra bit bigger, where the tolerance of the allowance should be as narrow as possible. In the gaussian curve, do not veer to the left nor to the right.
That precision is the model of how modern Israel needs to behave to achieve peace. Not giving in an extra inch to Esav any claim to the birthright, he schemed against his brother in humility. If he had to crawl, or beg Esav or Lavan, he did it to protect his birthright. It was like he had read Sun Tze's Art of War.
And the LORD saw it fit and precise that the nation of Israel should spawn with Jacob.