How can I protect myself from my chain of command in order to utilize Soldier for life career skills programs?

I'm going to be straight with you here: PCS to your next assignment and take SFLTAP there. Go for one of the bigger bases like Bragg, Hood, or JBLM that have very robust SFLTAP programs. Your CoC isn't required to sign off on your PTDY and let's be serious - USAREC has a reputation. It's not a fight you're likely to win.
But when you go to a BCT and you're just another KD complete SSG, it's a lot easier to lose one person who is already getting out.

This has nothing to do with EO. Your command knows, or should know what is REQUIRED by law for the Soldiers to transition. Its not much, DOL Workshop and VA briefings, the rest is optional. Some CoC are a little more liberal with what they will allow. As long as you make the MANDATORY requirements within the timeline they are doing their job. SFLTAP is not a free for all to do away with all of your military requirements until you ETS. If i were in your position, i would prepare a decision brief to give to your CoC, impress upon them the importance of what you want to do. Show them that you fully intend to meet your military requirements such as when you will take your PT Test, when you will qualify with your weapon, all still required until you ETS. Show them the importance and that you have a plan. This will give them a broader picture of what they can look forward to and how to best plan for your absence while attending this course you would like to attend. If you lay it all out in front of them they may still say no, but they just might say yes. Good luck to you.

EO covers unlawful discrimination specifically for the following categories: race, color, gender, religion, national origin, and sexual orientation.