Here is the refactored package structure. I have implemented standard logic for each component to ensure the code is functional and follows the Single Responsibility Principle.

### `queue/core.py`
Contains the foundational `Job` dataclass and the basic FIFO `JobQueue`.

```python
from dataclasses import dataclass, field
from typing import Any, Dict, Optional, Deque
from collections import deque
import uuid

@dataclass
class Job:
    """Represents a single job in the queue."""
    id: str = field(default_factory=lambda: str(uuid.uuid4()))
    payload: Dict[str, Any] = field(default_factory=dict)
    priority: int = 0  # Higher number = higher priority
    status: str = "pending"
    retries: int = 0
    created_at: float = field(default_factory=lambda: __import__('time').time())

    def mark_failed(self):
        """Increment retry count and update status."""
        self.retries += 1
        self.status = "failed"

    def mark_processed(self):
        """Update status to processed."""
        self.status = "processed"

class JobQueue:
    """A basic FIFO (First-In-First-Out) Job Queue."""

    def __init__(self):
        self._queue: Deque[Job] = deque()

    def add(self, job: Job) -> None:
        """Add a job to the end of the queue."""
        self._queue.append(job)

    def get_next(self) -> Optional[Job]:
        """Retrieve and remove the next job from the front of the queue."""
        if not self._queue:
            return None
        return self._queue.popleft()

    def size(self) -> int:
        """Return the number of jobs in the queue."""
        return len(self._queue)

    def is_empty(self) -> bool:
        """Check if the queue is empty."""
        return len(self._queue) == 0
```

### `queue/priority.py`
Implements priority-based ordering using a heap structure. It imports `Job` from `core`.

```python
import heapq
from typing import Optional, List
from queue.core import Job

class PriorityQueue:
    """A Priority Queue implementation using a min-heap."""

    def __init__(self):
        self._heap: List[Job] = []

    def push(self, job: Job) -> None:
        """
        Push a job onto the heap. 
        Note: In this implementation, lower priority number = higher priority.
        """
        # We store tuple (-priority, timestamp, job) to ensure heap order 
        # and break ties.
        # Using a counter to ensure stable sort if priorities are equal
        import uuid
        heapq.heappush(self._heap, (-job.priority, job.created_at, job))

    def pop(self) -> Optional[Job]:
        """
        Pop the job with the highest priority.
        """
        if not self._heap:
            return None
        
        # Unpack tuple to retrieve job
        _, _, job = heapq.heappop(self._heap)
        return job

    def size(self) -> int:
        """Return the number of jobs in the queue."""
        return len(self._heap)
```

### `queue/retry.py`
Handles the retry logic with exponential backoff. It imports `Job` from `core` and `PriorityQueue` from `priority`.

```python
import time
import math
from typing import Callable, Any
from queue.core import Job
from queue.priority import PriorityQueue

def process_with_retry(
    job: Job,
    task_func: Callable[[Any], Any],
    max_retries: int = 3,
    base_delay: float = 1.0
) -> bool:
    """
    Executes a task associated with a job, with exponential backoff retry logic.
    
    Args:
        job: The Job object to process.
        task_func: The callable function to execute with job.payload.
        max_retries: Maximum number of retry attempts.
        base_delay: Base delay in seconds for exponential backoff.
        
    Returns:
        True if successful, False if failed after max retries.
    """
    attempt = 0
    
    while attempt <= max_retries:
        try:
            # Execute the task
            result = task_func(job.payload)
            
            # If successful, mark job as processed
            job.mark_processed()
            return True
            
        except Exception as e:
            attempt += 1
            
            # Check if we exceeded max retries
            if attempt > max_retries:
                job.mark_failed()
                return False
            
            # Calculate exponential backoff: base_delay * 2^(attempt - 1)
            delay = base_delay * (2 ** (attempt - 1))
            time.sleep(delay)
            
            # Update job state for next attempt
            job.retries = attempt
            
    return False
```

### `queue/__init__.py`
The public API entry point. It imports and re-exports classes from the submodules to provide a clean interface.

```python
"""
Job Queue Package.

Exports:
    - Job: The dataclass representing a task.
    - JobQueue: Standard FIFO queue.
    - PriorityQueue: Priority-based queue.
    - process_with_retry: Helper for handling retries.
"""

from queue.core import Job, JobQueue
from queue.priority import PriorityQueue
from queue.retry import process_with_retry

__all__ = [
    "Job",
    "JobQueue",
    "PriorityQueue",
    "process_with_retry"
]
```