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

class JobQueue:
    def __init__(self):
        self.jobs: Dict[str, Dict[str, Any]] = {}
        self.backoff_sequence = [1, 2, 4]  # seconds
        self.max_retries = 3

    def add_job(self, job_id: str, data: Dict[str, Any]) -> None:
        self.jobs[job_id] = {
            "data": data,
            "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]
        data = job["data"]
        
        for attempt in range(self.max_retries + 1):
            try:
                processor(data)
                job["retry_count"] = 0
                return True
            except Exception:
                job["retry_count"] = attempt + 1
                if attempt < self.max_retries:
                    job["last_backoff"] = self.backoff_sequence[attempt]
                else:
                    job["last_backoff"] = self.backoff_sequence[-1]
        
        return False
```