Klrduks

I am flying from EUG to LAX on Alaska and LAX-DXB-AMS on Emirates. (All one ticket) As I see it, I have three main options:

1. Check my bags all the way through to AMS in EUG. This would allow me to stay air-side at LAX as you can now go from Terminal 6 to TBIT. This option would save me time at LAX but, as I am flying FC, my bags would not be tagged as FC for Emirates so it would take me longer in AMS to collect my bags. (In theory)

2. Check my bags in EUG to LAX only, collect my bags at Terminal 6 and re-check my bags with Emirates at TBIT. (I have a long layover so this would work.) This would mean going back through security at TBIT. This would cost me time at LAX but (again, in theory) save me time at my final destination.

3. Do option 2 but instead of going back though security at TBIT (assuming long lines and no priority line) go to T4 and go through priority security there as I am an American Gold.

Here are my questions

1. Which would you do?
2. Does TBIT have a priority security line for Emirates?
3. Can I use my AA Gold status to use the priority line at T4 with non-AA tickets?

Thanks in advance for your help.