I agree with Jonathan, he has several good points.
1. The copyright status of a critical text is a bit ambiguous, it probably hasn't been determined in court, especially for translations.
2. Why not just ask from copyright holders?
3. SBLGNT copyright holder could be more translation-friendly (see http://sblgnt.com/license/
). Their purpose was to create a text which was more free to use than NA.
4. The apparatus and headers are certainly under copyright.
What is presumed to be under copyright in the critical text itself is the collection of critical decisions, i.e. where the text differs from other texts. But here is the problem of the nature of a critical edition of any ancient text. Naturally where a part of the text, larger part than just a few sentences, follows some known ancient manuscript, it can't be under copyright. You can just copy from the manuscript text which is under public domain. But each reading in our critical NT texts is in some manuscript. How they can be copyrighted? Only the collection of the textual decisions, as far as they can't be reproduced mechanically using some algorithm or strict set of rules, can be under copyright. But the whole thing is uncertain legally because the copyright laws weren't made for this kind of situation.
The purpose of a modern critical text creates an ironical situation. The purpose is to find the "original" text, but if the critical text is actually the same as the original, it couldn't be under copyright. But because we don't have an autograph or a manuscript which represents exactly the original, a critical text can be under copyright as a unique non-copied work. As much as the copyright holders claim a critical text corresponding to the "original" they should renounce the copyright. For example in the UBS edition the A in the apparatus mean they are certain about originality (as far as I remember). If someone else copies their text in those places they shouldn't be able to sue the one who copied if they are intellectually honest. But what would happen if someone actually took the text of A certainty and e.g. made his own decisions only about the rest? I don't know, and nobody else can know either. You can either try or just ask of the copyright holders.
One possibility would be to take several modern critical editions (practically speaking NA, SBLGNT and NIV base text, maybe older WH and NA), copy what is common to them and make your own decisions about the rest (or just follow WH or older NA). I think it would be legally impossible to sue you because if it would be possible, some edition would already had violated the other's copyright, and I don't believe that's the case. Here we have to remember that the work behind the textual decisions can't be copyrighted, only the outcome which is the text itself. Therefore you can just copy the part (at least a large part) of the critical text which is identical to some other text. But this is speculation, IANAL and you're recommended to contact the copyright holders anyway.
Differences between SBLGNT and the Greek text reconstructed from NIV published as A Reader’s Greek New Testament: 616
Differences between SBLGNT and WH: 879
Differences between the Greek text reconstructed from NIV and NA/UBS: 231
(Data found in http://sblgnt.com/about/introduction/
You can see that you have to make relatively few decisions to make a unique work which doesn't violate copyrights. And this is for the Greek text only; in translation you don't have to show all Greek critical decisions. (On the other hand the base text of NIV is made in a different way - the number above tells how many times a decision is visible in the translation).
And don't forget the NET translators' notes. One could create a high quality critical text based on its notes, similar to the base text of NIV.