Inspired heroism (BTG)

first off, unless you are running a mill or graveyard combo deck, dedicated mill cards are a waste of mana -- cut mind grind. from there, you should probably cut a land and add 3 springleaf drum, the shinanigans with seer and siren will be worth it. i'd also cut 4 psychic strike for a third dimir charm and 3 syncopates or dissolves -- strike just feeds their deathrites, charm is REALLY good and the counters are also very solid. i'm tempted to recomend judge's familiar but i dont really know what to drop, maybe tormented hero, but hero might be good, not really sure. if you find hero to be lackluster in testing, give the bird a shot. i'd actually drop erebos -- i'd hate to hit him with seer, and his ability seems really risky what with 3 seer and 4 thoughtsweize already in main board -- for another another charm and another thassa or aqueous form. the unblockable stuff from thassa/form is great for inspired and the scry is nice. thassa lives through removal and is potentially a 5/5 late game, but form costs 2 less and triggers heroic -- they're both good, you can go with whichever. from their you can drop a specter for a third siren -- the inspired abuse may push it's value over that of specter.
I dont really understand what's happening in your sideboard. last thoughts and shadow slice are, to be perfectly honest, horrible. their cmc is way to high for seers, and their effects are not worth their cost. as stated above, mill cards are dead outside of a dedicated mill deck -- so phylax is bad. yes he turns on inspired, but the mill minuscule and irrelevant. i garentee that every serious standard game in which you find yourself using his ability as a win con you will lose. if you are so far behind that you are resorting to tap-mill, you're not gonna win. it's that simple. even if his ability was half decent, his cost of 5 is really scary for seer. i'm also confused about whip -- the lifegain is nice, but i it's ability is way too mana intensive for this deck. Elixir of immortality is solid lifegain and, to a certain extent, deathrite hate. i also dont really know enough about standard to know what would replace them, so leave 'em in i guess. The two things i full on agree with are the 2 bident (these are even worth 4 life off of seer) and 3 ashiok.
so after all that we now have a sb consisting of 2 elixer, 3 ashiok and 2 bident, leaving us with 8 open slots. from what i see, you will have some trouble with more agro decks due to the lack of removal. the obvious choice would be hero's demise, but if you want to keep it budget, some number of doom blade/pharika's cure/ultimate price would work. i'd also run the fourth seer for matchups where card advantage is key. that leaves you with 3 slots to do whatever you want with -- you could run your erebos's if you are worried about opponent's lifegain, more removal if your really concerned for agro, the final drum if you want the deck to go faster, or even the judge's familiar for the control mirror.
once again, really cool deck, and happy building!