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

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

    def add_job(self, job_id: str, data: Dict[str, Any]):
        self.jobs[job_id] = {
            "data": data,
            "retry_count": 0,
            "max_retries": 3,
            "last_backoff": None
        }

    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"]
        retry_count = job["retry_count"]
        max_retries = job["max_retries"]

        while True:
            try:
                processor(data)
                job["retry_count"] = 0
                job["last_backoff"] = None
                return True
            except Exception:
                retry_count += 1
                job["retry_count"] = retry_count

                if retry_count <= max_retries:
                    delay_index = min(retry_count - 1, len(self.backoff_delays) - 1)
                    delay = self.backoff_delays[delay_index]
                    job["last_backoff"] = delay
                    continue
                else:
                    return False
```