I tried the pre-approval link for years and never got anything to pop up. If you have a card that they are issuing that you really have a need for then just apply for it and get it over with. I did that and scored a 10K CL from them and opened the doors to all of their cards w/ lower risk of denial by being able to see the pre-approval status. Once you're in it's a different ball game completely because that denial seesaw goes away from the standpoint that it's a SP either way.
Basically I would go with the advice to apply for a card you want, without worrying about lack of preapprovals.
Preapprovals can give a warm fuzzy feeling, but as pointed out, they are not a guarantee of approval. And (as seen on this forum) they sometimes have an unfortunate effect of focussing the potential applicant on to those cards. Hence we see posts of the form "I'm preapproved for X from Bank A and Y from Bank B. Which should I get?" when frequently the answer will be, after much asking for spend and credit details, you will be better off with card Z from Bank C, even though you don't have a preapproval.
In the wider world, people generally will not know about preapproval sites, and will apply when they see an ad for a card that appeals (or respond to a targetted offer). And that usually works just fine!
Unless I am missing something (quite possible, not enough coffee in the world to keep me awake today) OP stated two reports are locked and one is frozen.
While one should not place too much weight on pre-approval or lack thereof, you cant get preapproval with invisible CR.
Unlock it, do pre-approval and lock it back if you have no plans to apply, or unlock, do pre-approval, grab a card, post approval thread.
Either way you'll need to unclock EX if Amex cards are still of interest to you.