I’ve had a similar experience. When I made first confession in several years, I also had a list of my previous sins which I wished to confess. Eventually, when I did confess it, the priest interrupted me as I was reading off the list, gave his spiritual direction, assigned my penance, and recited the prayer of absolution. While this appears to be somewhat more orthodox than yours, I was still perturbed by the fact that I could not complete my list of sins. When I did an online search of my circumstances, it appeared that the prayer of absolution was supposedly fully valid and I need not repeat my confession again.
Subsequently, I decided that the best answer would be obtained from my priest, not the internet warriors, and I consulted him. He understood my situation, and told me that I should confess my sins all over again, right from the top. He was a wonderful priest. He patiently allowed me to read my long list of personal sins racked up over the years, after which he gave me an equally long pastoral talk on the whys and hows in developing personal holiness to fight Satan. Subsequently, he gave me the prayer of absolution. It was probably the best and most cathartic experience I’ve ever had.
My advice to you is this: find another priest and explain your situation to him. We do not have the theological or pastoral insight to decide this for ourselves. The priest is best equipped to give you the necessary spiritual direction, and you should consider it. In a limited sense, priests are like physicians of souls - if you are ever in doubt, you may seek a second opinion, but you should not try to self-medicate.
This aside, I welcome you back into the fold of the Church! It is most befitting that yesterday’s parable spoke of the prodigal son. We celebrate your return and we pray for your continued development in faith.