I will bring a more revised version after I completed my tests.
I removed Cavern from the list because it did conflict a lot of times like expected.
Thornscape Apprentice is surprisingly good as a tapper and with Deathrite Shaman you have the option to activate first strike ability. But the important thing about being able to tap is that it goes well with the other disruption and with an active Ranger, you can control the board rather easily. For example you have an active Dryad Militant (yes running them alongside Deathrite Shaman) and you get in a tapper. At that moment an Oath player is in a tight spot. When he Oaths, he can lose key cards, the creature that comes into play will not be able to attack.
The most important thing about Deathrite Shaman are that the line of play we pointed out earlier: Being able to aggressively waste while providing mana by exiling their lands. Ssecond, it wrecks dredge with wasteland. Noble would not be able to do this. You take out Bazaar and cut them off dredgers. This alone is sometimes strong enough to win a game. The number of maindeck cards that also are ALSO good against dredge increased dramatically. Deathrite Shaman, Dryad Militant, Thalia and Wastelands.
I also don't think Mayor is the optimal card choice in such a deck, as a booster or clock. Mikaeus is better suited in this case with all the cheaply costed effective creatures.
Important to note that all three cards, Thalia, Dryad, Shaman, are disrupting Snapcaster Mage.
I believe Stony Silence (or maybe Null rod because it can come down under Golem? Is risking to pay

extra worth the 'immunity' vs other decks?) is a key card and stronger than Thalia (and combo's well with her obviously) to keep blue and shop off their mana. Because of the nature of this kind of builds, naturally strong versus other aggro (high creature count, mikaeus/ranger, first strike, shaman, safe vs wasteland...) you can totally afford to run 4x Null Rod. Also, mentioned earlier, the match versus dredge is also 'naturally' strong now. Just side in some Jailers and you will have a strong match up g2 and g3.
Lastly, I believe Deathrite Shaman gives us another relevant mana enabbler next to Noble. This allows us to run 6-7 1cc drops that help us win the mana denial war versus other decks using wastelands and it allows us to run a little less lands with Ranger and more threats. A good combination of ESG and mox is used alongside Stony Silence to have a clear and powerful plan versus any Workshop.