I don't understand your reply. I don't know what math you are using to show the conversions. What is the end product of the conversions you are showing. For example $156 = 0342, what is 0342, a DCS or a NAC digital? Also that conversion appears to be the opposite of what I'm talking about, which is converting a CTCSS tone into a decimal NAC. Your three conversions start with a hex NAC.
I also know that the CTCSS to hex NAC conversion used by NIFC and related agencies was prescribed by a standard conversion table the FCC proposed many years ago, but was not carried through to make it a requirement. As a result an agency could take a CTCSS tone, lets say 107.2 and use many different NAC's in its place. The NIFC/natural resource agencies as well as many fire agencies decided to use the proposed table anyway. So my understanding is there isn't a set mathematical relationship between the analog CTCSS and the hex NAC.
In the last two years, especially this year, I'm seeing quite a few channel plans that show repeater access tones where a CTCSS tone, of lets say 192.8 (NIFC Tone 16) having a digital NAC equivalent of 1928. The primary radio in use is the Bendix-King. I don't recall if any Motorola models are on NIFC's list of radios approved for use on wildland fires. Even the National Park Service, which utilizes digital more than any of the other land management agencies, provide BK radios for their fire personnel. In any case the BK can use the digital NAC.
The new national standard tone chart for the USFS and NIFC, which I've shown in the wiki pages of the National Incident Radio Support Cache, shows the CTCSS tone first, followed by the digital NAC and then the hex NAC. For those of us who have used the CTCSS tones for a lot of years and are familiar with the numbers it is much easier to remember that Tone 4, 136.5, is 1365 when using the digital mode of a radio system.