I don't know, but even if you retain that right, it seems almost obvious that you don't have the right to publicly bid for counsel. Presumably the gag order would extend to any lawyer you contact.
I do agree that the gag order would extend to any lawyer you contacted after the public bidding process concluded.
There is no clever loophole here, it's a very simple order. The law says "no [recipient] shall disclose to any person that the Federal Bureau of Investigation has sought or obtained access to information or records under this section." https://www.law.cornell.edu/uscode/text/18/2709
Here the definition of "disclose" is "whatever convoluted process you can think of".
Reading further, it does say you can talk to an attorney, but that doesn't mean you can make a Craigslist post asking for lawyers with experience in the Patriot Act.
https://supreme.justia.com/cases/federal/us/352/330/ (1957)
Further, it seems that Miranda only applies to custodial interrogations.
https://supreme.justia.com/cases/federal/us/384/436/ (1966)
I do think that if one is charged or restrained that the process might work. Of course, that's a pretty big escalation!
It seems like you're trying to hack in a domain that can't really be hacked, because it's not even very well defined. The spirit of the law is clear, I can't see any reason a judge would come down on your side of this. Prohibiting a bidding process does not restrict any of your rights.