Is there a name for this limit, no-check, poker game?

I have a poker buddy from South Carolina that introduced my local poker game to a high-low game he says they call “Pineapple” back home (but it’s not the ‘Texas holdem with an extra card’ game). There are no restrictions to which cards you can play to make your five card high and five card low hands (you can play all five in your hand or five cards from the board or any combination thereof).

Here’s how it is played:
Each player antes up a dollar and is dealt 5 cards.
First round of betting is in $5 increments - but there is no checking. You can only bet, raise, or fold. After the first round of betting, the first three cards of ‘the board’ are turned over. The action rotates, so if seat one started the action in the first round, seat 2 starts the second round.

Second round is also in $5 increments. Then two more board cards are turned over (we do it in a reverse pyramid instead of five across like in most Hold’em games, because there are more board cards to come). This starts third round, which is in $10 increments (remember, this is no checking allowed). Then one more board card is revealed.

Fourth round is $15, then the last board card is turned over and the final round of betting is $20.

Action is capped at 4 bets in typical limit fashion. Pot is split between High hand and low hand (8 or better).

I can’t find anything about this particular game on-line, and am curious if anyone else has played it or knows the proper name for it.