Putting children on the register of another class is not a valid way to deal with an infant class size problem.
Reclassifying which year children are in does not have any effect, quite apart from not being very sensible. Whilst we usually say the regulations apply to Reception, Y1 and Y2, they are actually based on age. They apply to classes where the majority of the children will attain the age of 5, 6 or 7 during the course of the school year regardless of which school year they are in.
If the school mix Y2 and Y3 such that the resulting classes have mainly Y3 children in them those classes are not subject to infant class size limits. They can then mix the remaining Y1 and Y2 children. That is the sensible approach to dealing with the problem without employing another teacher and is entirely within the regulations.
There are 8 categories of excepted children, i.e. children who don't count towards the class size limit. Children in two of these categories will remain excepted throughout their time in infants. Parents often think infant class size limits have been breached when in fact the presence of excepted children means they have not.
I don't know where you get your figure that "hundreds of schools are in default". I am not aware of any evidence that this is the case.
Enforcement is not down to the DfE. Local authorities carry the first responsibility for enforcing compliance. They are required to report to the Schools Adjudicator annually on whether or not all primary schools in their area are complying with infant class size regulations. Details then appear in the Schools Adjudicator's annual report and the Adjudicator ensures that LAs are working with the schools concerned to address any issues.
Some schools do, of course, fail to comply with the regulations. That will always be the case. There will always be schools/head teachers that think the rules don't apply to them. But the vast majority of primary schools do comply with infant class size regulations.