Medicare/Tricare Prime

Which process is most likely quicker?  If done outside of the military system (I'm looking and a band) can I get fills/adjustments at Madigan.  I'm looking into three surgeons outside of Madigan as well as Madigan.  Because of Medicare I have more options in as much that Tricare Prime doesn't require an approval because they are not the primary payer.  Right now I only have the one referral for Madigan but was told by my provider to let them know if I need another.