We have used Moog Lower Control Arm (LCA) on an Odyssey. It worked well, but I only used Moog since the OEM LCAs were so expensive. The OEM outer tie rod and the inner connected rod are pretty cheap so I would go with the OEM if you can. I think they are like $50 and $80, respectively.
At 10 years old, I do not think that you need any of the tie-rod replaced. If it is so rusted for real, then just replace the inner ball joint that connects to the outer tie rod.
The job is pretty easy, but you need the tie rod tool, which is cheap on Amazon.
https://www.youtube.com/watch?v=3DcAtFNEdxo
We used the Specialty Product Company to change the rear camber on the Odyssey. I think yours is SPC 67590 and they are $110 on Amazon. Make sure that you put lots of anti-seize on the bare thread to keep the bare thread on the SPC from rusting or else you will have to replace it again the next time that a shop needs to adjust the rear camber. I heard that the ball joint on the SPC is not as good as the OEM that is on the Odyssey, but I have not had any issue. Did the shop do an alignment and saw that the rear camber was off, then asked for you to install the adjustable rear arm?
Are you sure that the LEDs are shining at 9 and 3 o’clock with plastic base where the LEDs are attached to is locked in place vertically? The base where the individual LEDs light can rotate to any angle regardless of the how the LED base are twist lock onto the 9012 bulb socket.