Sure thing! Here's a Python code snippet that accomplishes the task you described using the `random` module:

```python
import random

def split_and_rearrange_strings(string_list):
    random.shuffle(string_list)  # Randomly shuffle the original list

    chunked_list = []
    chunk_size_range = range(5, 11)  # Range of chunk sizes (5-10 strings)

    while string_list:
        chunk_size = random.choice(chunk_size_range)  # Randomly select chunk size
        chunk = string_list[:chunk_size]  # Extract chunk from the original list
        chunked_list.append(chunk)  # Append the chunk to the chunked list
        string_list = string_list[chunk_size:]  # Remove the chunked strings from the original list

    random.shuffle(chunked_list)  # Randomly shuffle the chunks

    return chunked_list

# Example usage:
strings = ['apple', 'banana', 'cherry', 'date', 'elderberry', 'fig', 'grape', 'honeydew', 'jackfruit', 'kiwi',
           'lemon', 'mango', 'nectarine', 'orange', 'papaya', 'quince', 'raspberry', 'strawberry', 'tangerine', 'watermelon']

result = split_and_rearrange_strings(strings)
for chunk in result:
    print(chunk)
```

In this code, the `split_and_rearrange_strings` function takes a list of strings as input. It shuffles the original list, then iterates over it to create randomly sized chunks of strings (5-10 strings per chunk). The chunks are stored in the `chunked_list`. Finally, the function shuffles the chunks and returns the resulting rearranged list.

The example usage demonstrates how to call the function with a list of strings and print the resulting chunks. Note that the input list can contain any number of strings, and the code will adapt accordingly.
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