Haven't actually had a chance to play test the deck yet so not sure how it actually runs but I think it could have some potential. Any suggestions are very welcome ^^ please and thanks.
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Havengul Lich with perilous Myr can kill most of the big stuff in play right now by turn 4 3 mana out and pyrilous myr can be brought back 3 times for 6 damage with kills titans and that's just after turn 3.
and perhaps side board 4 surgical extractions yourself ^^
Might want to up the mental misteps to 4 cause I can see Surgical Extraction causing hugh problems otherwise.
We know but since your using Lich to recycle them forbidden alchemy is a great searcher turn 3 forbidden with any luck get your lich and dump a myr and solemn turn 4 cast lich (with heartless out) and since myr and Solemn are both in GY you can start recycling them
Ratchet Bomb would deal with the cage as well.
Steel Sabotage might be another option for dealing with the cage.
Sword can be risky in this deck since you've only got 2 creatures that aren't automatically dead due to Heartless summoning and you definitely don't want your Lich dieing.
Think I'd replace the think twice's with forbidden alchemy, quick way to get Myr or Solemn into your graveyard (best case scenario ^^)