for the most part I agree but a few things are rather bad Ideas I think.
first of all :
Netlag 350ms is on the one side to high and won't solve the underlying problem on the other hand.
Its too high because there are skills which have a cast time of 500ms, now if you have a netlag of 200ms that gives you 300ms to react meaning you can use items with instant cast, if we have a netlag of 350ms leaving you with 150ms to react its nearly impossible for most players to do this - and if you think that people shouldn't be able to counter a skill with 500ms cast time, replace it with a skill with 1 second cast time where the reaction time is decreased from 800ms to 650ms. Players with good reactions wouldn't suffer nearly as much as players without good reactions.
Besides of that 350ms is also a timespan where you already have a noticable delay from order --> execution which is rather annoying and will degrade the gaming experience. Demigod is not Supcom where it you control hundreds of units and have base building where it doesn't matter if the orders are executed a few hundred ms later and most people don't even really notice the delay, when you have a single Demigod and give them orders 350ms are very much noticable while 200ms or 250ms aren't.
Have you actually played a Demigod game with 350ms delay already? (for all who want to try : open the console with ~ (eng. layout) or strg+ö (german layout) and type net_lag 350. If you are playing a multiplayer game all have to do it to take effect.
It won't solve the problem because even 350ms is too low for europe - australia (usually 400 to 450) and sometimes for europe - south america (ranges from 300 to 450) as well. If we now assume that only 5% of the player population is from either australia or south america and 50% are from europe how big is the chance to have one of them in a automatch 5vs5? 1-(0.95^10)*1-(0.5^10) = about 40%. Exponentiation is a bitch. That is for random teams of course; arranged teams don't nearly suffer as much from this problem, at least when europeans don't team up with australians.
From that perspective you'd either need gateways, remove the random team option, ban australians from playing it or need to come up with a better idea than increasing net_lag to 350ms. 350 ms also isn't that good because the range 250ms to 350ms is nearly unoccupied - its either below 250 or higher than 350 mostly, at least for europe, I have no clue how its for north America. Its a very unpleasant topic but ignoring that issue won't help and it needs a good solution.
Dynamically setting the net_lag would be certainly an option, while I wouldn't want to play every game with 350ms net_lag I'd prefer it over stuttering and slowdowns when there is actually someone in the game with a high ping. Either automatically or just via an ingame option as it is done in starcraft: anyone can change it and it takes effect for all when only one changes it. I don't buy this "people will abuse it and grief with that feature", it works for starcraft why shouldn't it work for other games. Even abusers and griefers don't enjoy stuttering. A game lobby option would be useless for automated matches as there is no lobby (at least I guess there is no one). Have a low (200ms), medium (300ms) and high (400 or 450ms) delay setting in the connection menu (F11).
No matter what you decide definitely keep the manual override via console in.
You maybe should also consider setting the net_lag for singleplayer to 20ms. You might say that it is a bad idea because people will cry that multiplayer is less responsive than singleplayer but Blizzard uses a lower netlag for singleplayer than for LAN and a lower netlag for LAN than for Battle.net and when it comes to things like this I think you should just copy their approach instead of thinking that you know it better.
compared to that issue all other points are pretty minor:
Requested new item: Scroll of Invincibility
Unit is invincible for 3 seconds
Instant cast time
Cost: 200
maybe you forgot a zero at the end, because for 200 this item is crazy, it allows everyone to safely teleport back home without any chance to kill him. It also makes Oak a lot less unique and there is enough stuff which keeps you alive already in the game and having completely invulnerable enemy running over the maps all the time is at least as annoying as multi-stun. If you want a new defensive item it should be more special like : "Unit can't be hurt from normal weapons" or "all damage is capped at 50 per shot/effect" (Damage over time would still do 50 damage every tick then).
I like that "5 second invulnerable but you also get 5 second stunned" Trinket a lot, it doesn't allow to flee but it can get your cooldowns ready, heal you up a bit (especially as Sedna) or buy the 5 seconds your allies need to get you out of the mess.
The rook moves far too fast by default. He’s a walking castle! Super tough but super slow.
speed is a very sensible matter, before 2C rook was at speed 6 when all others were at speed 7 which really made rook annoying to play especially as he is a melee character. In 2C all Demigods were speed 6 which obviously was bad. In 2D rook has speed 5.7 when all others have 6.0 as base value, which might be still a bit too fast but anything below 5.5 would probably make it really tough for rook to actually ever use his melee attack vs another Demigod (unless that other Demigod is melee and chooses to pick the fight). Having a lower base speed also means that speed items are less effective on him than on other Demigods, so if you lets say reduce his speed to 5.0 he would be outrun so badly in later game stages that he wouldn't be enjoyable anymore. He might be a walking castle but it is a magic walking castle.
Being slower for a melee character already means that he can't retreat without getting hits.