I would put Pot of Avarice in the side deck.
I don't see much of a use for Apprentice Magician and Old vindictive Magician.
Best for this deck to be a full Tomato Control.
Depends on his style of play... for aggression, go Tomato to gain access to Don Zaloog and Stein. For a more balanced approach, go apprentice magician together with the 2 OVA and the 1 MOF.
(Honestly, I think that Newdoria is weaker than OVA in the context of which one is better if it's special summoned by their respective recruiter... of course it's better to summon in def mode than attack mode if they're both used for defense. But, both of them can stop Hydroggedon, but Newdoria pays 400 LP to do it which isn't much.)
If you got stein already, then having Lily at the same time seems redundant... Personally, the way I see it, is that Lily is a more flexible, less extreme version of Stein. Both of them relies on a direct attack. Both costs LP. Lily's payment comes only when the attack is successful but it's hardly as destructive as stein. Both of them works mostly by the same exiled-will search, so it seems redundant here... Lily is generally used as the "counter-stein" by knocking off heavy LP, and can stall out the Cyber Twin (but sadly not the Cyber End unless you also got rush) if there's no limiter. Since you seem to like Stein more, put Lily away for something else...
However, yeah it seems difficult to use both toolbox at the same time... I'll personally pick tomato too because its synergy is better with your particular sidedeck.
So...
-1 Apprentice Magician
+1 Mystic Tomato
-1 Old Vindicative Magician
+1 Newdoria
-1 Injection Fairy Lily
+1 Newdoria
Also, I will never see Pot of Avarice as a +1 on the basis of using one card (-1) to draw two (+2). If you're recycling monsters, those monsters are all potential +1s because they're usually either recruiters which can generate advantage by calling more monsters, or they will save your sorry butt by recycling powerful topdecking choices when the momentum is not in your favor (Cyber Dragon.) Assigning an advantage number to Pot of Avarice is a terrible injustice for its life saving or further aggressive potential (watch your enemy cry when 3 hydros go back to the deck in mid game.)