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Based on what I've heard about the LMI product, I do not believe it is related to gorilla's PVA wood glue. It's a ANSI/HPVA type II water resistant product, and LMI is clearly a uncatalyzed PVA that will readily dissolve in water when dry. I ran some competitive tests for a project a little over a month ago to evaluate its performance.

Results from ASTM D-905 Shear Strength Competitive Testing (Reported as Avg. ± 90% Confidence Interval):
Test articles were assembled from hard Maple, Acer Saccharum, and tested in a MTS Universal Tester with a 100kN load cell.

Titebond II
Room Temperature: 3922 ± 160 PSI
150°F Overnight: 1718 ± 110 PSI

Titebond III
Room Temperature: 3467 ± 280 PSI
150°F Overnight: 1295 ± 464 PSI

Elmer's Max
Room Temperature: 2255 ± 259 PSI
150°F Overnight: 1158 ± 52 PSI

Elmer's Carpenter's
Room Temperature: 3655 ± 530 PSI
150°F Overnight: 981 ± 300 PSI

Gorilla Glue
Room Temperature: 1263 ± 269 PSI
150°F Overnight: 698 ± 169 PSI

Gorilla Wood Glue
Room Temperature: 3393 ± 203 PSI
150°F Overnight: 1727 ± 173 PSI

I have not tested Gorilla Wood Glue's water resistance claim, but it is a well performing product from a strength perspective. Keep in mind that strength at elevated temperature correlates directly to creep resistance. Most people are unfamiliar with confidence intervals. They are a statistical calculation similar to margin of error. All of the values reported above therefore describe that the true value, lies within ± CI of the calculated average with 90% certainty. Due to wood variation, good test results typically have confidence intervals of ~20% the average.

Let me know if there are any questions.