I say yes the Coupon Type 1's are part of the T206 set. The Type 2&3's are part of a completely different company. I have explained below how I came up with this "crazy" notion.
The ATC owned the rights to the Type 1 Coupons and were printed as part of the T206 set in mid 1910 approximately. The cards were made by the ATC as part of their advertising campaign in cigarettes, and they were printed with all the same inks and designs. Nothing we have can disprove this theory. The thin paper argument can be explained in part to moisture. The thinner paper stocks that were made in the southern areas was likely due to the decrease in mold or mildew issues due to high humidity. Many southern advertisements have been found with the thinner paper stocks from that time frame. Thinner paper stock holds way less moisture and therefore will not be destroyed a fast as heavier card stock that has the ability to absorb and hold moisture from the air.
The ATC was divide into several sections when it was split up on May 29, 1911 ; Liggett & Myers(LM) being the main focus of my post. LM was given control of the W. R. Irby, New Orleans factory #3. This factory more than likely was forced to change the designs of the subjects that they once printed under the ATC banner due to Copyrights. The change in design had to be significant enough to not violate those laws and thus we have the major changes such as paper stock, inks, colors, back designs, cropping, players, ect. I also believe the glossy coating was to help offset the moisture absorption of the cards. Seal the front side and it reduces the amount of surface that can breath and thus make the card more moisture resistant. This also can help explain the cracking of the coating from the card stock expanding and contracting over the many years from different moisture environments.
We all need to stop and take a step back to look at what we have compared to what Burdick was trying to piece together. The internet and research of thousands of guys creates a much more detailed map. Best guess is that Burdick decided to combine them all into one group most likely due to some backlash he would have feared to receive from the LM company. Back then the company name would have been much more respected than now over 100 years later. LM was an instant powerhouse right out of the gate and any man no matter the riches or stature would have been fearful of disrespecting them back then in any way, especially in a published book for the public to use. The laws were much different then especially knowing that LM's history would later reveal some shady dealings throughout their inception from the ATC dissolution. I am sure you can imagine judges and lawmaker taking kickbacks to obtain bias towards them. I mean that never happens now or anything
You also wouldn't call a Dodge Hemi Cuda a Chrysler even though its owned by them. We respect the original company manufacture and it would be sacrilege to call it a Chrysler ___ ___.
The same should be done with the card sets. We should recognize them for what they are. ATC owned the Coupon T206's and LM had the Coupon's for 1914 and on under a different company and new branding campaign.
My research with fellow members has led us down several paths but realistically the simplest explanation seems to be the best:
"W. R. Irby, New Orleans factory #3 was owned by two different companies at two separate times. Due to this, cards produced before the ATC dissolution, mid 1910, were produced for distribution in the T206 advertising campaign. The cards produced between 1914-1919 were part of another brand and thus would be forced to change designs significantly enough as to not violate copyright laws of the time".