The way it's going to be played is that you will go for spread Balance + spread Spear in every Divination window.

The fact that you cycle through all cards at least once means that either Ewer or Spire is automatic fodder for Royal Road in order to spread either Balance or Spear. So two cards are already decided. They will be played at the end and stacked with the next Divination.

Your thought process will be to ignore Bole and Arrow and look at: Spear, Ewer, Balance, Spire.
You want them in a permutation where Balance and Spear are not next to each other. This is a 1/3 chance of a favorable permutation. That's pretty bad, so using Shuffle here is not the best.

Your safest bet becomes to wait for one of the four cards and put it into the appropriate slot. Say you draw Ewer - which you Royal Road. Then if Spire comes up, you Shuffle, otherwise you lose your 2nd spread.
Your chance now is 2/3 for a favorable permutation of the other three cards.
Considering Divination + 2 Shuffles, you have three shots to get that favorable permutation. The probability for that is around 96%.

Everything else is "whatever" because the spread dps cards are simply too powerful.

Time Dilation, you just hold and use 2 charges for each spread card.
Minor Arcana is worthless.
Sleeve Draw is a more of a detriment. The only possible benefit is that you can get a spread dps card + Divination in the opener, but the chances are not good enough to make it worthwhile in normal play. Every other Divination is stacked and you'll want to delay your first spread dps card for buff windows rather than speed it up.

I ignored Arrow as a dps card because it's annoying and everyone rightfully hates it for causing misalignment. It also makes probabilities easier to understand. That said, it's probably still better than a single spread in that window.

So my question is, what is the goal behind this system?
Because if your intention was to encourage people to use Support cards, it's not going to work. My current opinion about Support cards is that they have to be completely divorced from DPS cards in order to create a healthy system.