Is there anything in the literature that supports revolutionary claims for this "new" sulfuric-acid battery?
There is nothing in the chemistry of what they describe that is different in any way to a conventional Lead-Acid battery. What they really seem to claim is improvement in materials in the battery not to change the electrochemistry but to improve other aspects of battery operation. For example:

MEG's E-SOURCE™ power cell technology is based on a lead-fiberglass composite material that is one-third the weight and 50 times the strength of metal alloys used in conventional batteries. To date, more than $100 million has been invested in research, development, manufacturing, and market testing of this technology in the United States and several international markets.

This suggests they have built a better lead-acid battery rather than something more radical. This is not ridiculous. They claim the following advantages:


Extraordinary manufacturing and user cost savings
Significant weight reduction compared to conventional lead-acid    batteries
Exceptionally long service life
Dramatically fast recharge speeds at all operating temperatures
Safe, simple, and low-cost maintenance


It is not impossible to imagine clever overall design and improved microstructural components and electrode materials could deliver these sorts of improvements and it is certainly far easier than inventing a whole new battery electrochemistry. For example, charging speed is often dominated by the physical material properties of the electrodes and not the underlying electrode chemistry, so clever design can mitigate the physical limits on charging speed such as by increasing the effective surface area.