First question, and it is going to make me sound like an @$$hole, but I am gonna ask anyway. If you were on the ship for 2 years, and your conversion package took 6 months, does that mean it took 18 months to ultimately fail BNEQ? I ask because you are only alloted 24 months to qualify Senior-in-Rate, which in your case would be SRO. If this is the case, you were severely behind the curve in your expected qualification progression.
Now to something not potentially controversial.
If I recall correctly, TAPS is not guaranteed.
What IS required, by law, are the briefs on what VA benefits you are entitled to upon separation. The other stuff concerning interviewing, resume writing, etc. is not part of the deal.
And yes, they most certainly can give you two weeks notice that you are going to be unemployed.
Also, your Career Counselor/Chain-of-Command failed you IF they did not brief you on the highly unlikely chance of your force conversion being approved. With a high percentage of other rates being either at or above required manning levels, the chances of converting after being de-nuked are almost nonexistent.
Lastly, along with the other advice given here don't forget to look into unemployment. This is an involuntary separation, not due to bad conduct so you may be eligible until you get into college or get employed elsewhere.
Best of luck and thank you for volunteering to serve.