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This might sound difficult, but I sense you should temporarily re-route the plumbing so it is off the joists. This would allow you to properly jack the existing structure and add new. Your pictures will help determine if this is the best direction to take.
Remember the jacking process must be slow to minimize damage and maximize adjustment within the framing and walls. A 1/4 turn per day on your jack posts is often recommended.
Once you have achieved the desired leveling, you can bring in new joists as stand alones or sister them to your existing joists. This should fix your problem ....