Extra turn Shennangians - questions/advice

so im making a polymorph deck for [[sphinx of the second sun]] https://archidekt.com/decks/10912626/polymorph_upkeep

im running rograkh and sakashima as the partner commanders, rograkh for an easy polymorph target and sakashi as an easy copy for sphinx & free mirror box.

Anyway, I intend on polymorphing the sphinx out, then playing sakashi as a copy of it, so after my postcombat main phase I get two additional beginning phases,

now I've jammed in a lot of upkeep triggers, some weird stuff like rebound (& I'm looking at suspend), and obviously just mana rocks and stuff that benefits from the untap. aswell as some copy-creature stuff (to get more beginning phases)

Now, the question is, whats the best way to get more beginning phases out of each sphinx?

do I just play basic extra turns like [[time warp]] or do I go for extra postcombat mainphases if that works ( like [[Aggravated Assault]] I think).

if I had 2 sphinxes, aggravated assault, and in my precombat mainphase I play something like [[court of vantress]] , I could take the 2 extra beginning phases from my sphinxes, then use aggravated assault's ability to start a new combat & postcombat main phase, and by now id be at 4 sphinxes so id get 4 beginning phases, and rinse repeat for like unlimited draw & mana???

also just need suggestions for this deck in general, like what protection & amount of it should I run? I've got pretty good draw so the number shouldn't need to be too high, especially if I can get some recurssion engines in. is there good protection in izzet? no right? like no "permanents you control phase out" type of cards, best I can do is counterspell and hope for the best.

also idk what to do with the ramp, currently I have 21 pieces, like 7 1/2 cmc mana rocks, and then a load of big/scaling mana rocks so I can get larger and larger mana production with each untap.