I'm in the middle of my second playthrough and have completed 5 of the "Recover XYZ Object" missions... not mentioning what they are for spoiler purposes.
The strategy that works best that I have found (At least for my playstyle) is to...
1: Clear a direct path between your Homeworld and the object's system.
2: Capture these systems with Logistics CC's. Place forcefields on the wormholes leading back to your Homeworld.
2: Break your fleet into two "Contingents"; one as the escort contingent, the second as the Mobile Contingent.
1a: Use the Escort Contingent to stay with the escorted object at all times. It is usually best to split it up over the current system's inlet points so as to kill AI ships as they come through, meaning less targets for your ships to simultaneously target, meaning more of your ships fire on a smaller number of their more powerful ones. If you're not finding success with this, keep the whole of your Escort Contingent with the shard to work as a group. Engineers in FRD are very useful as well.
1b: Use the Mobile Contingent to work ahead of the shard. This keeps the AI's forces split among two systems, letting you divide and conquer. It keeps pressure off of your Escorts and the shard while helping to prevent some AI ships from rushing to your homeworld.
3: Set your spacedocks to send all produced ships to the fray with rally points. Avoid ships that take a long time to produce like Bombardment or Beam frigates. I usually pick very fast-producing or high-capacity ships to keep numbers high (Cannon Fodder Doctrine). The function of this practice is self-explanatory.
Just keep pushing on. If you set things up correctly, the AI will be slowed down with the presence of the Logistics CC's and the forcefields they have to break through to get closer to the shard.
*Phew*, Glad that's over.