I applaud you for taking it so seriously. Many people don’t even go, so it’s refreshing to read about someone who treats it with the respect that you have for it.
I think if you feel the need for a confession as you described, then it would be important to schedule a private confession with a priest. If a particular parish or priest is unwilling to schedule an appointment then perhaps you should consider a different priest. The place where confession is held all day might be a grew place to start. To me it shows that they also take the sacrament very seriously and want to allow as much time as possible for people to use it. Perhaps you could show up before that one opens and get a good spot in line.
Don’t be too scrupulous about making sure you name every single one of your sins. If you happen to forget one genuinely, know that God will still forgive you even if you do not have a chance to confess it.