The ShiftstonedEternal Power Calculator is a deck-building tool that visualizes your odds of drawing enough Influence and Power based specifically on the cards found in your deck.
I'm not sure if a deck that contains cards from three different campaigns can be called "Budget". Haven't played it yet, but three campaigns are pretty expensive, don't you think?
Gold has always seemed fairly easy to get but your argument is fair. You can't get away from getting Into Shadow since this is a Maul deck, but Equivocate can be swapped out for Edict of Grodov. Saber-Tooth Prideleader is a flex spot in the deck. I was originally running Darkbolt and it was doing a fair amount of work. Though Swirl the Sands could be a better option if you are seeing a fair number of relics and fliers.