Hand 1: If he is truly a maniac and his range for pushing like this is wide, then your hand crushes his range and warrants a call.

Hand 2: What position is the solid player calling from? If he is in late position/SB and I really think he can make that call with AJs/AQs and low/medium pairs I will surely overpush. If hes UTG+1 I really doubt he would be calling here with these hands, but if maniac has been doing this for a while and I feel this guy may be fed up, that may slightly change things. Sure you may "only" be a coinflip, but theres a pretty big overlay on your coinflip from Mr. Maniac, and ill gladly take a coinflip with all of that dead money. There are 6 hand combinations that have you dominated given your holding, and the only time you would be making a big mistake considering the dead money is if you knew solid player had AA, as even against KK you are 30%. Even if we give solid player a REALLY tight range (QQ/KK/AA/AK) then you are against 9 combinations of AK for likely split, 3 combinations of AA for a dismal win %, 3 combinations of KK for 30% (which isn't even THAT terrible given the dead money, as you are getting 1.7:1 on your push and are 2.3:1 to win), and a coinflip against 6 combinations of QQ getting that huge overlay. I don't really see how overpushing in this spot could be too bad.