Here's the complete refactored package with clean separation of concerns, proper relative imports, and a well-defined public API.

### `queue/__init__.py`
```python
"""Public API for the job queue package."""

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 structures and base FIFO queue implementation."""

import time
import uuid
from dataclasses import dataclass, field
from typing import Any, Optional
import queue as std_queue


@dataclass
class Job:
    """Represents a unit of work to be processed."""
    id: str = field(default_factory=lambda: str(uuid.uuid4()))
    payload: Any = None
    priority: int = 0
    status: str = "pending"
    created_at: float = field(default_factory=time.time)


class JobQueue:
    """Base FIFO queue for processing jobs."""
    
    def __init__(self):
        self._queue = std_queue.Queue()

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

    def dequeue(self) -> Optional[Job]:
        """Remove and return the next job from the queue."""
        try:
            job = self._queue.get_nowait()
            job.status = "processing"
            return job
        except std_queue.Empty:
            return None

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

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

### `queue/priority.py`
```python
"""Priority queue implementation using a min-heap."""

import heapq
from typing import Optional
from .core import Job, JobQueue


class PriorityQueue(JobQueue):
    """Processes jobs in priority order (lower number = higher priority)."""
    
    def __init__(self):
        self._heap = []
        self._counter = 0  # Monotonic counter to preserve insertion order for ties

    def enqueue(self, job: Job) -> None:
        """Add a job to the priority queue."""
        heapq.heappush(self._heap, (job.priority, self._counter, job))
        self._counter += 1

    def dequeue(self) -> Optional[Job]:
        """Remove and return the highest priority job."""
        if self._heap:
            _, _, job = heapq.heappop(self._heap)
            job.status = "processing"
            return job
        return None

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

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

### `queue/retry.py`
```python
"""Retry logic with exponential backoff."""

import time
import logging
from typing import Callable, Any, Optional
from .core import Job

logger = logging.getLogger(__name__)


def process_with_retry(
    job: Job,
    func: Callable[[Job], Any],
    max_retries: int = 3,
    base_delay: float = 1.0,
    max_delay: float = 60.0
) -> Optional[Any]:
    """Execute a job function with exponential backoff retry logic.
    
    Args:
        job: The job being processed.
        func: Callable that accepts a Job and returns a result.
        max_retries: Maximum number of retry attempts.
        base_delay: Initial delay in seconds before first retry.
        max_delay: Maximum cap on delay between retries.
        
    Returns:
        The function's return value on success, or None after all retries fail.
    """
    last_exception = None
    
    for attempt in range(max_retries + 1):
        try:
            result = func(job)
            job.status = "completed"
            return result
        except Exception as e:
            last_exception = e
            job.status = "failed"
            
            if attempt == max_retries:
                logger.error(f"Job {job.id} failed after {max_retries} retries: {e}")
                break
                
            delay = min(base_delay * (2 ** attempt), max_delay)
            logger.warning(f"Job {job.id} attempt {attempt + 1} failed. Retrying in {delay}s...")
            time.sleep(delay)
            
    return None
```

### Key Design Decisions:
1. **Single Responsibility**: 
   - `core.py` handles data modeling and basic FIFO operations
   - `priority.py` isolates heap-based ordering logic
   - `retry.py` encapsulates resilience patterns
   - `__init__.py` acts as a clean facade

2. **Import Strategy**: Uses relative imports (`.core`, `.priority`) to avoid circular dependencies and keep the package self-contained.

3. **Interface Consistency**: `PriorityQueue` inherits from `JobQueue` to guarantee method signature compatibility, but overrides internal storage to use `heapq` instead of `queue.Queue`.

4. **Production Readiness**: Includes type hints, docstrings, logging, status tracking, and capped exponential backoff to prevent runaway delays.

You can now use the package like this:
```python
from queue import Job, JobQueue, PriorityQueue, process_with_retry

queue = PriorityQueue()
queue.enqueue(Job(payload="task1", priority=1))
queue.enqueue(Job(payload="task2", priority=0))

job = queue.dequeue()
result = process_with_retry(job, lambda j: j.payload.upper())
```