I like both your ideas above regarding extra copies and minimum decksize.
I feel +2 / +3 for duplicates is too much but haven’t tried building a deck yet. +1/+2, or even the MWL’s straight +1 each, both seem cleaner from a design standpoint though.
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Regarding influence and deck construction - I haven’t played Commander, but I feel as though the faction restriction proposed at top is excessive due to the way that influence contrasts with colors in MtG: Having a multi-color Commander does open up more card pool but including additional colors brings the burden of having mismatched cards and mana sources in the early game. However, in Netrunner, there is effectively no downside to importing a card across factions. Having such a restriction in Netrunner deck construction to a single faction would limit deck flexibility (yesterday I died to meat damage from a standard Palana deck!) and we can see from Custom Biotics that having such a restriction comes with a corresponding influence benefit.
(I don’t like the term Commander for netrunner cards either, I’m going to use the term Locus here instead to mean “Region or Console” until someone comes up with a better term).
I think a good workaround for respecting the desire to somehow limit construction would be to allow cross-faction Locus selection, but giving a “flexibility” influence bonus for picking one in-faction and an influence restriction for picking one out-of-faction (which I understand is similar to the Fealty vs. Banner system used in Game of Thrones).
My idea here is built off of using the blank influence pips from the original post.
Choose an ID, then choose a Region / Console from any faction as a Locus. With respect to the ID faction, count the out-of-faction influence pips on the Locus. The deck must have at least (4 x pips) influence spent on cards from the Locus’ faction. The deck may spend (4 x in-faction/blank pips) additional influence that cannot be spent in the Locus’ faction. (If the Locus is in-faction or neutral, the deck gets 20 extra influence.) Corp decks may contain agendas from the ID faction or the Locus faction.
The number 4 could be adjusted if playtesting reveals it to be too extreme or too limited. I like, though, that it nearly prevents Midway Station Grid (influence of 4) from being used as a Locus outside of NBN, especially given that higher influence values are supposed to correlate to being representative of a faction. As another example: a Professor / Desperado deck becomes constrained to require 12 influence spent on Criminal cards, and given 8 extra influence for other non-criminal faction cards.