Chinwoo-er,
Why not Mantis?
Even the Shaolin temple supports that Fuju invited 18 masters to Shaolin around the beginning of the Song(960-1279) Dynasty.
The styles and names of teachers were preserved at that time.
This is in Shaolin records as well as Mantis which has preserved an in depth version of the old manuscripts.
The dates and stories can't be verified through normal historical channels.

Though all undateable the writing style as well as choice of characters suggest great antiquity.

After the Song, Shaolin MA fades from the spotlight, not to appear until middle to late Ming(1368-1644).
Here is where the fame of Shaolin stick fighting starts.
The story of Shaolin stick can easily be traced to the Yuan(1260-1368)(maybe earlier by others)when written material appears.
The originator of Shaolin stick-we are talking Yuan legend here-was a cook who used his stick to beat invading bandits.
The legend later claims him to be Jinnaluo.

It has been rewritten at different times with different names and details though.

Shaolin's big fame with the stick began in the Ming with the manual Exposition of Shaolin Stick(one of the best and most important CMA books ever written).
Though there are also verifiable accounts prior to this of the greatness of Shaolin stick.

The Longfist derivitives such as Hua Chuen, to my knowledge, aren't mentioned until Chi Ji Guang's military training manual of mid Ming dynasty.
Though it first appears in the alleged Fuju's account of 18 masters.

In this book other styles such as Eagle Claw are also mentioned.

A book on Shaolin published in early Ching(1644-1911) but with roots to late Ming gives a different picture of Shaolin pugilism.
This book details Mi Chuen, which, to my knowledge, is not practiced by Shaolin temple anymore.

Scythefall,
The methods descended from Shaolin are vast.
Many legit schools of Shaolin can easily not include any of your mentioned requirements.

To determine if the MA is genuine Shaolin:
-Prove to some extant the date of Fuju's 18 masters and clearly show where the descended over the past hundreds (thousand?)of years.

-Show how a master studied at Shaolin as in ngokfei's case.
-anymore?