These are mostly equivalent, but...
Trainer got stuck in traffic so we will start at 11 am.
This comes off as a bit more strict. It doesn't leave a lot of leeway for the idea that "starting" is a process that could take a while. You get the sense that a person who would speak this directly would perhaps be the type of person to be mad if everyone wasn't attentive and ready to go at 11:00 A.M. exactly.
Trainer got stuck in traffic so we will be starting at 11 AM.
The "will be starting" is the more easy-going sounding way that people would say it. Here a "start" isn't a description of something happening in an instant...it's a state of "starting" that you can "be" in--for some amount of time.
Most people would probably go with "starting" here. But really, it's a pretty subtle distinction.
It's not standard English. The article says that it's from a North Carolina (U.S. Southern) dialect.
There are many, many regional variations on standard English grammar and vocabulary, often called "dialects". They're usually not accepted in formal writing for a broad audience. Schools usually teach children to avoid the nonstandard words and grammar, at least in a formal setting; more here.
The article is mainly concerned with how to explain "double auxiliaries" in terms of transformational grammar. Simplifying for brevity: This is a theory that all grammars of all human languages are instances of a single, mathematically pristine set of rules for generating all possible grammatical sentences. This "universal grammar" is postulated to have various "switches" that different languages turn on and off, accounting for the differences between different languages' grammars. If you're thinking that this is a dubious theory, you're not alone, but this is a matter on which people can reasonably disagree. Anyway, for the theory to be true, the postulated transformational grammar must be able to generate every possible grammatical sentence in all languages and all their dialectal variations, and be unable to generate any ungrammatical sentence in any language or dialect (given appropriate switch-settings). If the nonstandard grammar of the North Carolina dialect allows a sentence that the leading transformational grammar can't generate, this is evidence disproving the theory or else requiring that the transformational grammar be modified to include it. The article is mostly concerned with how to make this revision. From p. 12:
…given McCawley's
framework, the difference between the standard dialect and the double
perfective dialect can be captured as a difference in the ordering of the two cyclic rules, Tense-Replacement and Attraction-to-Tense. Since these rules are both cyclic, either can apply. In the standard dialect, Tense Replacement precedes Attraction-to-Tense; in the double perfective dialect, Attraction-to-Tense can precede Tense Replacement. This alternative ordering
generates both the will had and will have had forms.
So, the information is true, but it does not mean that the future pluperfect is standard English.
Best Answer
Definitely not. Perfective progressive (perfect continuous) is a combination of perfective and progressive aspects. Perfective indicates anteriority to some time, and progressive implies duration/temporariness. It has its uses in modern English.