Wow, that is a big one, just a mess.
I don't recommend that clients approach these types of issues as being "correct" or not but rather think about how far you want to take it and the costs.
There are a lot legal issues involved for which I would need to collect more facts and do more research prior to giving a conclusion. You certainly have an argument that some or all of your names are not dilutive. Did you use the name in commerce before getting the letter?
The first thing to consider are the risks of standing firm. Are you willing to go on with a lawsuit for this? Clearly they are spending some legal dollars on this and creating lots to litigate. The federal registration of your exact name (and assuming they have no intention of using it) raises a host of questions. Also, while you like the name, how valuable is it to your business? Some of it seems important like the Austin Shops part that you may want to negotiate even if you are willing to forgo the Bearded part. Put another way, how much time and energy do you want to devote to keeping the name rather then developing your business.
Bottom line is this question is fairly complex and not one for which you should take answers in this forum. You should go see a lawyer with trademark experience in Austin and soon. If you are reluctant to do that, then you have the answer to your question.
Normally, we are able to negotiate a settlment that allows firms to do business without the expense of litigation. The strategy behind that is not something you would want discussed in this public forum, which you should presume is being read by the lawyers who sent you the letters. From what you describe, you should obtain confidential representation quickly.
The following is not legal advice and should not be relied upon to take or refrain from taking any action.
As noted by other respondents, if you're serious about doing business under any "Bearded Ladies" mark then you need to speak with a Texas-licensed attorney -- who should also respond to the cease and desist letters that you've received.
To prepare you for that meeting:
Forget about who filed what with whom when. While there may be some Texas-law specific procedural benefits from such filings, at the end of the day the question of which of you has the greater legal right to use a "Bearded Ladies" mark depends on the respective trademark rights that you two have actually created through the use of a mark. Filings create procedural rights, use of a mark creates substantive rights.
Through its use of "Bearded Lady" over the years, the screen printing company has established trademark rights in that mark and all marks that are confusingly similar and which will likely confuse consumers in the marketplace.
Based on your facts it appears that you've yet to use a "Bearded Ladies" mark in commerce and so you currently have no trademark rights (or if you've used it in advertising only, then only weak trademark rights). Your various filings demonstrate an "intent to use" a mark for which the screen printing company could properly respond. It's filings to reserve various trade name rights are generally irrelevant (as are yours). In short, the screen printing has a significant leg up on you in this dispute.
The issue, as you note, is whether your use of "The Bearded Ladies Present" would infringe the screen printing company's trademark rights (forget about dilution -- the screen printing company's mark is not "famous" which is a prerequisite to a dilution claim).
Courts in Texas use a particular multi-factor test to evaluate whether infringement (based on the likelihood of consumer confusion in the marketplace) has occurred. The one who is accused of infringement is not in the best mental frame of mind to objectively assess whether his or her mark infringes but you can read a typical infringement analysis here: http://www.altlaw.org/v1/cases/1673025 Envision your mark instead of the defendant's and see where you come out on the matter -- and then have a trusted aunt or friend do the same thing.
Note: You need to evaluate your proposed "Bearded Ladies" logo use seperately from your use of a "Bearded Ladies" trade name. My gut reaction is that using the logo as a mark (so long as it does not also include the literal element "Bearded Ladies" ) would likely be non-infringing. As for using a "Bearded Ladies" trade name or any trademark containing that literal element, my gut reaction is that the screen printing company has a pretty good argument that such use would be an infringement.
Now you're ready to speak with your lawyer.