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That's my understanding too, i.e. the parent swtich must be in VSS mode, although you don't actually need the pair.
Also correct, as each IA parent can host 42 switches, at 48 edge ports per switch, that's up to 2,016 IA ports per distribution, or your 8,064 for four of them.
Besides the 6807 and 6880 the 6840 is supposed to support IAs too.
Lastly, although you noted many of your IDFs don't have the fiber runs to support multiple stacks, if you did have those runs, you also have the option of activately using up 8 links per IA stack.
PS:
Although you asked about IAs, again if your fiber runs are limited, you could use a stackable switch like the 3650 or 3850 in the IDF. You can stack much larger or cascade stacks in the IDF.
