```python
from typing import Callable, Dict, Any

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Dict[str, Any]] = {}

    def add_job(self, job_id: str, payload: Dict[str, Any]) -> None:
        self.jobs[job_id] = {
            "payload": payload,
            "retry_count": 0,
            "last_backoff": 0
        }

    def process_job(self, job_id: str, processor: Callable) -> bool:
        if job_id not in self.jobs:
            return False
        
        job = self.jobs[job_id]
        max_retries = 3
        backoff_sequence = [1, 2, 4]
        
        # Initial attempt
        try:
            processor(job["payload"])
            return True
        except Exception:
            # Retry loop
            while job["retry_count"] < max_retries:
                job["retry_count"] += 1
                # Calculate backoff (simulated storage)
                backoff_index = job["retry_count"] - 1
                backoff_duration = backoff_sequence[min(backoff_index, len(backoff_sequence) - 1)]
                job["last_backoff"] = backoff_duration
                
                try:
                    processor(job["payload"])
                    return True
                except Exception:
                    continue
        
        return False
```