“The legally free working population” versus “pre-existing middle classes”

This distinction is central to your argument.

Suppose before emancipation there are already:

• merchants;
• professionals;
• shopkeepers;
• manufacturers;
• wealthy farmers.

They may already constitute parts of a middle or intermediate social class.

That is not the population you are tracing.

You are tracing:

formerly unfree person → legally free worker → working class → some upward movement → middle class.

Therefore, the formation of the legally free working population is one historical question.

The formation of the pre-existing middle classes is another.

For example:

“Industrialization increased the number of merchants.”

That tells you about merchants.

But your question is:

“Did some people who entered the working population after emancipation subsequently rise into the middle class?”

The first proposition does not answer the second.