I can see why give the statue to the opponent so you can get Raviel back to hand, but you still need 3 tributes to get him back on the field. Something like Tsukuyomi or that Lv12 Subterror monster to flip down Raviel is better so you can re-flip summon Raviel once per turn work better.
Tri-Wight provides the Tributes. (Assuming you fix the deck in the way I mentioned, of course.) Recycle puts it back into the Deck, and it has 2 copies so you can use it every turn.
Flip Summoning Special Summon monsters like Raviel doesn't count towards the number of Summons for their mats. You need to properly Summon it each time for it to count.
Is this correct? Since we got subterrors, I have been able to get the mats by flip summoning monsters to get their mat. Maybe the game has glitched on me? Your description sounds accurate for summoning extta decks monsters from the GY.
Flip Summons count for Normal Summon monsters like Insect Queen and Blue-Eyes I believe. I'm like 99% sure they don't work for monsters like Raviel, Harpie Lady Sisters or Stardust Dragon.