the flush with WD40 is the only fix you (or any mechanic) can really do. If you have a broken return spring, you can't buy the part and Shimano does not even recommend repair (they want you to buy a $$$ replacement brifter, go figure!).
Good news is the flush-out frequently works. You *can* do a little disassembly to help expose the innards for flushing, but yes, special tools (TL-ST01, TL-ST02) are required for both take-apart and reassembly, and it won't really help the cleaning that much.They recommend you re-grease one inner surface, but in reality if the WD40 works you can just go forward without new grease and prepare to use the WD40 again, when needed.