But there is a deeper philosophical issue with your idea of the scientific method :
Consider what is meant by independent replication. Does it mean that the experiment must be repeated from scratch with different material etc. such that it is an independent test from the previous attempt?
Or does it mean that it has to be repeated by different people as well ?
It raises a conundrum. If people are a factor that must be controlled for by this definition, no replication can ever occur since the exact individuals that performed the experiment will have changed by definition during this 'replication' attempt. The skill and knowledge of people is a factor that is notoriously difficult to objectively quantify. This often results in statements such as "X method/assay/procedure does not work well in our hands ".
On the other hand , if people are not a factor, then replication of the experiment by the same group of people will also qualify as an independent replicate.