Not running Samnite in Phantom Glads is a waste. It's like not giving a damn for easy mass pluses (destroy opponent monster, draw 1, get Gladiator card, +3) :P. At least I would recomend you to test it.
2 Icaruses works nice with 2 Lanista, 2 Equeste, 1 Bestiari and 2 provings, so 3 would work pretty well with 3 Lanista, 2 Equeste, 1 Bestiari, 3 Provings to search any, 2 Duality...
Remember you can tag to a winged beast if you have Icarus set so...
Besides, 3 Equeste is just nuts IMO.
-1 Equeste, +1 Samnite.
-1 Lanista, +1 Gale (Lanista/Icarus can't deal with Stardust, Gale can on it's own, plus it can be food for Icarus)
I would take out Heavy Storm for 1 Judgment. 3 Typhoons are enough s/t hate this format, specially in a control based deck where you run plenty of backrow.
-1 Heavy, +1 Judgment.
That would be all. I'm just a bit afraid of monster mashes with 14 monsters + 3 proving but I guess it's ok for you.
Looks nice overall.
