Given the fact that Solomon veered away from Loyalty to YHWH, and even served other gods, what should we think about Solomon's eternal destiny?

Two Reasons lead me to believe that Solomon is among the redeemed

1. Solomon is the author of several chapters of the Bible. Would God have used an apostate to write Scripture? That seems unlikely to me

2. Solomon appears to be the author of Ecclesiastes. This book seems to have been written later in his life given the fact that he A) gives advice to the youth, and B) he reviews his many accomplishments.

At least two pieces of Ecclesiastes appear to show that Solomon had a genuine change of heart as he grew into an old man.
First, in Ecclesiastes 2:1-11, Solomon is seen denouncing his lifestyle of sinful indulgence

• I said to myself, “Come now, I will test you with pleasure. So enjoy yourself.” And behold, it too was futility. ² I said of laughter, “It is madness,” and of pleasure, “What does it accomplish?” 
• ³ I explored with my mind how to stimulate my body with wine while my mind was guiding me wisely, and how to take hold of folly, until I could see what good there is for the sons of men to do under heaven the few years of their lives. 
• ⁴ I enlarged my works: I built houses for myself, I planted vineyards for myself; ⁵ I made gardens and parks for myself and I planted in them all kinds of fruit trees; ⁶ I made ponds of water for myself from which to irrigate a forest of growing trees. 
• ⁷ I bought male and female slaves and I had homeborn slaves. Also I possessed flocks and herds larger than all who preceded me in Jerusalem. 
• ⁸ Also, I collected for myself silver and gold and the treasure of kings and provinces. 
• I provided for myself male and female singers and the pleasures of men—many concubines. ⁹ Then I became great and increased more than all who preceded me in Jerusalem. My wisdom also stood by me. ¹⁰ All that my eyes desired I did not refuse them. I did not withhold my heart from any pleasure, for my heart was pleased because of all my labor and this was my reward for all my labor. 
• ¹¹ Thus I considered all my activities which my hands had done and the labor which I had exerted, and behold all was vanity and striving after wind and there was no profit under the sun.

Second, at the end of the book, Solomon hits the meaning of life dead center:

• ¹³ The conclusion, when all has been heard, is: fear God and keep His commandments, because this applies to every person. ¹⁴ For God will bring every act to judgment, everything which is hidden, whether it is good or evil. (Ecc. 12:13-14)

So For those reasons, I think the best answer is that Solomon is in fact among the redeemed