All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
First of all, we say that what we mentioned in the fatwa which you referred to is recommended and not obligatory. So the imam is not sinful if he supplicates with the singular pronoun.
As for your question: "Is it allowed to use both these singular and plural forms when I pray alone?"
Then we say that most narrations of Al-Hassan ibn ‘Ali, may Allah be pleased with both of them, in the hadith about the Qunoot supplication are in the singular form: "Allaahumma ihdini feeman hadayt, wa ‘aafini feeman ‘aafayt..." and some of them were in the plural form: "Allaahumma ihdinaa feeman hadayt, wa ‘aafinaa feeman ‘aafayt..." as in the narration by at-Tabaraani in Al-Kabeer and by Ibn Hibban in his Saheeh. It is better that you supplicate sometimes with the singular form and sometimes with the plural form. As for combining both the singular form and the plural form in one supplication, then we do not see any harm in doing so, and you should not be strict about this, as it is a flexible matter, so do not waste your time and our time with such questions.
As for your question about whether or not the narrations of At-Tabaraani and Ibn Hibbaan are authentic, then the narration by Ibn Hibbaan was authenticated by Al-Albaani and Shu‘ayb Al-Arnaa‘oot. As for the narration by At-Tabaraani, then we did not come across any scholar who ruled whether or not it is authentic or weak, but its chain of narrators includes Al-Hasan ibn ‘Ali ibn Shahrayaar, about whom Ad-Daaraqutni said, "He is weak." Also, its chain of narrators includes ‘Ali ibn Sa‘eed ibn Basheer Ar-Raazi, who was classified by some scholars as weak.
Following is the version of the supplication with the plural pronoun:
"Allaahumma ihdinaa feeman hadayt, wa ‘aafinaa feeman ‘aafayt, wa tawallanaa feeman tawallayt, wa baarik lanaa feemaa a‘tayt, wa qinaa sharra maa qadhayt, innaka taqdhee walaa yuqdha ‘alayk, innahu laa yathillu man waalayt wa la ya‘izzu man ‘aadayt, tabaarakta rabbanaa wa ta‘aalayt."
Allah knows best.