Here's the complete refactored package structure with production-ready implementations:

### `queue/__init__.py`
```python
"""Job Queue Package

Public API exports for clean consumption.
"""
from .core import Job, JobQueue
from .priority import PriorityQueue
from .retry import process_with_retry

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

### `queue/core.py`
```python
"""Core data model and basic FIFO queue operations."""
from dataclasses import dataclass, field
from typing import Any, Optional
from collections import deque
from datetime import datetime


@dataclass
class Job:
    """Represents a unit of work to be processed."""
    id: str
    payload: Any
    priority: int = 0
    status: str = "pending"
    created_at: datetime = field(default_factory=datetime.now)
    retries: int = 0
    max_retries: int = 3


class JobQueue:
    """A basic FIFO job queue."""
    def __init__(self):
        self._queue: deque[Job] = deque()

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

    def dequeue(self) -> Optional[Job]:
        """Remove and return the first job in the queue."""
        return self._queue.popleft() if self._queue else None

    def is_empty(self) -> bool:
        """Check if the queue contains no jobs."""
        return len(self._queue) == 0

    def __len__(self) -> int:
        return len(self._queue)
```

### `queue/priority.py`
```python
"""Priority-aware queue implementation."""
from typing import Optional
from .core import Job, JobQueue


class PriorityQueue(JobQueue):
    """Orders jobs by priority (higher value = higher priority)."""
    
    def enqueue(self, job: Job) -> None:
        """Add job and maintain descending priority order."""
        self._queue.append(job)
        # Sort in-place by priority descending
        self._queue = deque(sorted(self._queue, key=lambda j: j.priority, reverse=True))

    def dequeue(self) -> Optional[Job]:
        """Remove and return the highest priority job."""
        return self._queue.popleft() if self._queue else None
```

### `queue/retry.py`
```python
"""Retry logic with exponential backoff and jitter."""
import time
import random
from typing import Callable, Any, Optional
from .core import Job


def process_with_retry(
    job: Job,
    processor: Callable[[Job], Any],
    max_retries: Optional[int] = None
) -> Any:
    """Execute a processor with exponential backoff retry logic.
    
    Args:
        job: The job to process
        processor: Callable that accepts a Job and returns a result
        max_retries: Override job's default max_retries
        
    Returns:
        The result of the processor
        
    Raises:
        The last exception if all retry attempts are exhausted
    """
    retries = max_retries if max_retries is not None else job.max_retries

    for attempt in range(retries + 1):
        try:
            return processor(job)
        except Exception as e:
            job.retries = attempt + 1
            if attempt == retries:
                raise e
            # Exponential backoff with jitter to prevent thundering herd
            backoff = (2 ** attempt) + random.uniform(0, 1)
            time.sleep(backoff)
            
    return None
```

### Key Design Decisions:
1. **Single Responsibility**: `core.py` handles data modeling & basic FIFO, `priority.py` handles ordering logic, `retry.py` handles fault tolerance.
2. **No Circular Imports**: `core.py` is dependency-free. `priority.py` and `retry.py` only import from `core.py`.
3. **Thread Safety Note**: The base implementation uses non-thread-safe structures for simplicity. Add `threading.Lock` or use `queue.Queue` if concurrent execution is needed.
4. **Clean API**: `__init__.py` uses `__all__` to explicitly define the public interface, hiding internal module structure from consumers.
5. **Extensibility**: `PriorityQueue` inherits from `JobQueue` but can be replaced with a heap-based implementation if O(log n) insertions become necessary.