Must I re-perform the missed prayers that I performed out of sequence, or what should I do to make up for missed prayers, and which of the sayings of the Four Imams should I adopt, knowing that I did not observe the sequence between the missed prayers themselves, nor between the missed and the current prayers?

You are not required to re-pray missed prayers without order. It is sufficient for you to maintain future prayers at their proper times and to arrange what you have missed. We have clarified in our recent fatwas that the order among missed prayers is not obligatory. If you wish to be strict with yourself and re-pray those prayers, the matter is up to you, but we do not advise you to do so.