Technical feature of the American Telephone and Telegraph (AT&T) convertible issues

In the book SECURITY ANALYSIS (Principles and Technique) 6th Edition by Benjamin Graham and David Dodd, there is a chapter (Chapter 24) about the TECHNICAL ASPECTS OF CONVERTIBLE ISSUES. Therein exists a part that I cannot fully understand:

A Technical Feature of Some Convertible Issues. A technical feature of
the American Telephone and Telegraph convertible issue deserves
mention. The bonds were made convertible at 180, but, instead of
presenting $180 of bonds to obtain a share of stock, the holder might
present $100 of bonds and $80 in cash. The effect of such an option is
to make the bond more valuable whenever the stock sells above 180
(i.e., whenever the conversion value of the bond exceeds 100). This is
illustrated as follows:

If the stock sells at 360, a straight conversion basis of 180 would
make the bond worth 200. But by the provision accepting $80 per share
in cash, the value of the bond becomes 360 – 80 = 280.

This arrangement may be characterized as a combination of a
conversion privilege at 180 with a stock purchase right at 100.

[Conversion mechanics]
The conversion privilege, as a concept, is clear: a bond of par X may be converted into N shares of stock, giving the shares a price of Y(=X/N) for the convertible owner. What I understand from the first sentences is that the owner of the example bonds (par value not mentioned) has the option to convert them to stock at a price of $180 of bonds per share, i.e. if bond par X = $1000, then N = 5.555 shares at a price of Y = $180 can be afforded with a single bond. Is this the correct conclusion thus far?

[Conversion with cash]
What I also gather is that, instead of exclusively providing (converting) bonds as "payment" for the shares, the owner could also add cash to cover part of the transaction. So for a bond par X = $1000, N = 6 is possible if $80 are added in cash and Y = $180. Is this a correct understanding?

If so, are the $80 a fixed amount (i.e. "no more, no less")? Are they per share, per bond or per transaction?

Separately, these two "illustrative" sentences are a complete mystery to me:

If the stock sells at 360, a straight conversion basis of 180 would
make the bond worth 200. But by the provision accepting $80 per share
in cash, the value of the bond becomes 360 – 80 = 280.

[Bond worth with hybrid conversion] Firstly, how can the bond be worth $200 if the stock sells at $360 and the bond can be converted to a stock at a price $180 of bonds per share – that looks like the owner is giving $180 for $360? Secondly, how does the option of adding cash to the transaction somehow add value to the bond? Lastly, how should one read this calculation: 360 – 80 = 280?

I strongly believe that there is something fundamental that I misunderstand in the whole example. It would be great if somebody can point that out, so maybe all the questions above can be answered by simply making that clear.