1) Which part do you think is nit picky when comparing like-to-like?
Perhaps nit picky is the wrong term. Too worried about the rules as a way to restrict the player characters rather than guidelines with which to guide improvisation?
* 3 * Group checks (just like it would be Reduced Effect and impose * 3 moves in Blades given the distance)?
That part is odd to me, because IME it would stay 3 checks, but likely a longer conversation about approach, because...that is a weird way to approach that situation. Sprinting across isn’t going to make it more likely you succeed. 5e PCs would instead be angling for advantage on as many checks as possible, rather than fewer checks. Things like the ranger or Druid casting PWOT or the rogue going first at a higher DC to give other advantage by showing the stealthiest path, the Wizard analyzing optimal weight distribution to avoid creaking or other excessive movement of the ladder, etc.
* Willingly knocking that down all the way to 1 * Group Check (rather than 2 * Group Check) after the "lets run across" action declaration? That seems like as favorable a ruling as there could be.
Again a more normal ruling IMO would be to just give advantage on some of the checks, or let certain characters just succeed due to their approach. IME
* Enforcing Heavy Armor penalties for Stealth (Disadvantage)?
IME DMs are split on how much they enforce that one.
* Int vs Spell DC for mechanical advantage (Advantage) via distraction by way of Silent Image (that is orthodox Silent Image)?
This is where still imposing disadvantage on heavy armor PCs is very restrictive here, because Advantage and Disadvantage cancel out. 5e isn’t so permissive that it’s a good idea to limit PCs beyond what the rules do.
* Using the Hard DC of 20? I would absolutely expect that from a HUGE cluster of 5e GMs given the factors of the situation outlined. In fact, I could see GMs bumping that to 22 or north. 20 seems like the floor given the factors.
The floor would be about 15, IMO. They’ve got a lot of advantages, they should all either have Advantage or at least straight rolls, and they’re not really doing soemthing crazy.
* The only thing I can see at nit-picky (which is why I caveated it as such) is the "but what about you moving silently with Invisibility...Invisibility doesn't give you full stealth...you're just unseen" clause. But my guess is a HUGE number of 5e GMs would go with that clause.
2) Whichever you disagree with above, do you think that most 5e GMs would agree with you?
Not really salient to my point, which was admittedly tangential to the point of your post. However, I think it would be a rough split.
For anyone who consumes a lot of actual plays, it would be split along lines of those who DM like Mark Hulmes (High Rollers. Very by the book, oppositional to the PCs in terms of rulings and construction of adventures, with a mindset of supposed impartiality, but often showing disappointment when his monster doesn’t gank someone)
vs
DMs who DM like Brennan Lee Mulligan (Dimension20. Has referred to DMing as an act of service, views the DM as “another person at the table”, and has as his overwhelming priority the fun and joy of his players. Very into honoring the creativity of the players while presenting them with fantastical people and places, improvisation, and ruling with a bias toward the rule of cool, and not letting RAW get in the way.
I think this forum skews more one way than the general gaming community does.