Here is the refactored package structure. I have inferred standard implementations for the classes and functions based on the names provided to ensure the code is complete and functional.

### Directory Structure
```text
queue/
├── __init__.py
├── core.py
├── priority.py
└── retry.py
```

### 1. `queue/__init__.py`
This file exposes the public API. It imports specific components from the internal modules to keep the package namespace clean.

```python
"""
Job Queue Package.
Provides a structured job queue with priority support and retry mechanisms.
"""

from .core import Job, JobQueue
from .retry import process_with_retry

__all__ = ['Job', 'JobQueue', 'process_with_retry']
```

### 2. `queue/core.py`
Contains the `Job` dataclass and the main `JobQueue` orchestrator. It handles the business logic of the queue, relying on the `PriorityQueue` for ordering and `process_with_retry` for execution.

```python
import uuid
from dataclasses import dataclass, field
from datetime import datetime
from typing import Any, Callable, Optional

from .priority import PriorityQueue

@dataclass
class Job:
    """Represents a single unit of work."""
    payload: Any
    priority: int = 0  # Lower number = higher priority
    job_id: str = field(default_factory=lambda: str(uuid.uuid4()))
    created_at: datetime = field(default_factory=datetime.now)
    status: str = "pending"  # pending, processing, completed, failed
    metadata: dict = field(default_factory=dict)

    def __lt__(self, other):
        # PriorityQueue comparison logic
        if self.priority != other.priority:
            return self.priority < other.priority
        return self.created_at < other.created_at

class JobQueue:
    """Main queue orchestrator managing job lifecycle."""

    def __init__(self, max_retries: int = 3):
        self._queue = PriorityQueue()
        self.max_retries = max_retries

    def enqueue(self, payload: Any, priority: int = 0, **metadata) -> Job:
        """Add a job to the queue."""
        job = Job(payload=payload, priority=priority, metadata=metadata)
        self._queue.push(job)
        return job

    def dequeue(self) -> Optional[Job]:
        """Retrieve the highest priority job."""
        return self._queue.pop()

    def peek(self) -> Optional[Job]:
        """View the next job without removing it."""
        return self._queue.peek()

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

    def process_job(self, job: Job, func: Callable) -> bool:
        """
        Execute a function against a job with retry logic.
        Returns True if successful, False if all retries exhausted.
        """
        if job.status != "pending":
            return False

        try:
            result = process_with_retry(func, args=(job.payload,), max_retries=self.max_retries)
            job.status = "completed"
            return True
        except Exception as e:
            job.status = "failed"
            job.metadata['error'] = str(e)
            return False
```

### 3. `queue/priority.py`
Implements the underlying heap data structure. It keeps the queue logic decoupled from the specific heap implementation details (e.g., `heapq`).

```python
import heapq
from typing import Any, Optional

class PriorityQueue:
    """
    A min-heap based priority queue wrapper.
    Jobs with lower priority values are dequeued first.
    """

    def __init__(self):
        self._heap = []
        self._counter = 0  # To ensure FIFO order for equal priorities

    def push(self, item: Any, priority: int = 0):
        """Add an item to the queue."""
        # We store a tuple: (priority, insertion_order, item)
        entry = (priority, self._counter, item)
        heapq.heappush(self._heap, entry)
        self._counter += 1

    def pop(self) -> Optional[Any]:
        """Remove and return the highest priority item."""
        if not self._heap:
            return None
        _, _, item = heapq.heappop(self._heap)
        return item

    def peek(self) -> Optional[Any]:
        """Return the highest priority item without removing it."""
        if not self._heap:
            return None
        return self._heap[0][2]

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

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

### 4. `queue/retry.py`
Handles the exponential backoff logic and execution of functions.

```python
import time
import math
from typing import Callable, Tuple, Any, Optional

def process_with_retry(
    func: Callable, 
    args: Tuple = (), 
    kwargs: Optional[dict] = None, 
    max_retries: int = 3, 
    base_delay: float = 1.0
) -> Any:
    """
    Executes a function with exponential backoff retry logic.
    
    Args:
        func: The callable to execute.
        args: Positional arguments to pass to func.
        kwargs: Keyword arguments to pass to func.
        max_retries: Maximum number of retry attempts.
        base_delay: Initial delay in seconds.
        
    Returns:
        The result of the function.
        
    Raises:
        Exception: The last exception raised if all retries fail.
    """
    if kwargs is None:
        kwargs = {}
        
    last_exception = None
    
    for attempt in range(max_retries + 1):
        try:
            return func(*args, **kwargs)
        except Exception as e:
            last_exception = e
            if attempt < max_retries:
                # Exponential backoff: base_delay * (2 ** attempt)
                delay = base_delay * (2 ** attempt)
                time.sleep(delay)
                
    raise last_exception
```

### Key Refactoring Decisions:
1.  **Separation of Concerns**: 
    *   `priority.py` handles only the heap mechanics.
    *   `core.py` handles the business logic (Job definition and Queue orchestration).
    *   `retry.py` handles only the execution strategy (backoff timing).
2.  **Circular Import Prevention**: `core.py` imports `PriorityQueue` from `priority.py`. `priority.py` does not import from `core.py`, preventing circular dependencies.
3.  **Type Hinting**: Added standard `typing` hints to improve IDE support and maintainability.
4.  **FIFO Stability**: The `PriorityQueue` uses a counter to ensure that jobs with the same priority are processed in the order they were added (FIFO), preventing starvation of older jobs.
5.  **Public API**: `__init__.py` acts as the facade, allowing users to `import queue` and access `queue.JobQueue` directly without importing internal modules.