I honestly don't experience a difficulty spike at all.
The only spike I hit is the end of D where I get bored of the character and stop paying attention XD
TBH I'm now a somewhat decent player (recently completed a
lairless DelverDs), so maybe I wouldn't notice the difficulty spike.
Your guide looks like it introduces massive unnecessary difficulty spikes, each time you change god. Honestly just don't do Crypt if you can't do it without TSO (unless you want the Hell runes). Ely is perfectly fine for the whole game. Especially don't switch out of Ely before getting the Vaults rune. V:S is one of the places where Ely really shines, because no-waiting health gain is very good when you can't stairdance. Also Elf can -often but not always- be done a lot earlier, and Slime is -often but not always- easier than V:$. If you want an easy game it's usually worth doing both Slime & V:$.
The branches you pick should depend on your character. Orc needs MR, Elf is easy if you have all (or most of) the resistances, Spider needs rPois, etc. Of course you still need to have enough xp, even if you are set up well for a branch, and you can complete any branch with a unappropriated character if you're overleveled enough. (ie if you have no resistances but you've made it to XL 27 you can probably do Elf). Slime and V:$ need one of a large set of very specific strategies, and you need to build your character towards such a strategy. (ie Ignition for Vaults, or stealth+melee for vaults, or Ely+Melee for Vaults, there's many more)
On the whole I agree with braveplatypus, that dying in Vaults & Slime & Elf is currently part of learning to play DCSS, and maybe it doesn't need to be.