Hi James.
In regards to your questions, I wouldn't say Meyer's longsword is a true two hander in the sense of a Spadone or Montante. Granted, big longswords did become common during this time and existed along all manner of standard longswords and bastard swords, and Meyer's "style" does seem to favor slightly longer weapons, but I would say that some of his guards and cuts would be impossible with the enormously sized weapons.
As for favoring cuts in the longsword section, this serves a twofold purpose. Firstly it allows Meyer more page space for instruction on various types of cuts and devices that a two handed weapon would favor over the single handers he introduces later along with your standard cuts. Once the rappier and dussack come around, you have their cuts as well as their thrusts included in his teachings (this is of paramount importance in the rappier section).
Also, his lack of thrusting as well as his inclusion of flat strikes is indicative of the social mandates of the period. In some German towns of that era, laws stated that street duels/brawls were to be started with flat strikes to first contact to avoid any unnecessary bloodshed. If the fight was of a more serious nature, the edge would be permitted to conclude upon first blood. If the aggressor continued from the first bleeding wound, then use of the thrust was permitted to put them down once and for all, provided one was willing to face the judicial consequences that would follow from taking a life in a nonsanctioned duel (which could be considered manslaughter or murder depending on your personal conduct and witness testimony).
So with that said, if you want to start two handed sword work, Meyer would be an excellent source to study from, and coubled with an appropriate large sized longsword foil like the Pavel Moc Type C (which is based on a 16th Century original federschwert from Germany, and allows for the flat strikes with much greater ease than other foils out there), you will have a great means to achieve your groups goal. I will advise that if you REALLY want to grasp true two handed sword material, it wouldn't hurt to branch out and study from the aforementioned Italian sources you listed above. You will find greater insight that help not only in studying other facets of the Art, but will help you better understand the material you started with by looking at if from another vantage point!

At least that's how its worked for me so far!
Good luck in your endeavors, my dear friend!
Regards,
Ian
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