I get that the deck can mill but tutelage does seem out of place and a bit of a pain to splash for (it's the only blue card period which begs the question if it's actually worth that effort). Considering the number of ways you suggested the deck can win, it seems like it would be more beneficial to stick inside the primary colors.
Now regarding cards, did you try or consider
Vampiric Rites or
Altar's Reap? Seems like either could be a good fit. Same with
Mortuary Mire. If you're sac'ing as much as it seems, trading some swamps for additional recursion might be worth while.
Shadows of the Past and
Graveblade Marauder would like all the sac's too. Like Auunj said, splinters seems like it could be considered. I also have a tough time not including
Nissa, Vastwood Seer in any deck that plays green, and wondered if she deserves a spot.
elk
I've tried them all, except mire - but I'd be worried about going over 6 comes into play tapped lands. The inclusion of tutelage takes exactly one potentially blanked land slot, and can kill in two/three turns. The deck is stupid fast. I've ko'ed the opponent three times on turn six, and one of those was via mill. It's a secondary wincon that is extremely hard to avoid, because turns 6-10 you can easily 'draw' 5-6 cards per turn (e.g. Mill 10-12 cards at least), and you can set it off at any time by sacrificing all of your board presence. Moreover, all the extra draw happens as a consequence of trying to win via the primary win-con. So either way, at all times you are playing both mill and beatdown at the same time.
Basically tutelage turns this into a very fast combo deck.
Plus, when you draw that much, you don't care if a couple cards are duds. You will draw into the mana you need, and you will eventually draw into the cards - opponent depending - that will seal the deal.
Don't think you really need recursion in this deck, although I could totally understand the thought process. Shadows is too slow, Graveblade marauder doesn't do anything this deck doesn't already do better. Nissa is awesome, but too slow, IMO for this deck. But I certainly wouldn't mind fitting her in. I just can't think of anything I'd remove (and I want this deck to be as consistent as possible).
Edit: just an added thought... This deck can certainly support some alternate wincon concepts thanks to all the draw. So I really like the tutelage concept, because once it goes off its basically uninterruptible - it's too quick, and it happens at instant speed, so even if they have Felidar Cubs, so long as you play around them, it's going to be GG. But all of that said, I think the engine is robust enough that some minor changes can still easily be supported in the build - e.g. Putting in a Nissa, or switching out something for ulamog, etc...