If you run the continuous trap "Xyz Veil", there is no window and your Basiltrice will be untargettable already on summon. Then you can put more overlay units and it'll be untargettable not depending on Xyz Veil.
To use xyz veil you need to wait a whole turn, setting a non disruptive trap and passing is a sui cide, in the other hand if you do summon basiltrice first turn a simple Samurai destroyer, overflow, the spider desperado uses and Verre can beat it.
Unless you are lucky and attach 5 materials first turn
It's not the only thing to set. You need a good hand to also set a disruption against those monsters and they not having a good hand that removes those disruptions. Xyz Veil is to stop their target disruptions from disrupting Basiltrice before you put the 4th and 5th overlays. But it's hard to get 5 overlays quick anyway.
1 Pillar + 1 Peryton + 1 Hydra + 1 other hazy
Activate Pillar, normal summon Peryton, special summon Hydra and Sphynx from deck by tributing Peryton and discarding Hydra on hand, activate Sphynx effect and revive Hydra from gy, if you get lucky and flip a hazy from Sphynx effect you can get 6 in 1 turn, or else 5 at most.
A better option would be to use generic backrow removal cards. Continuous trap is too slow in the current environment, while we're waiting for that 1 turn to pass, most of the decks we face can just otk us without a sweat.
Those decks can’t just run over Basiltrice that has got a hand with a field to protect it. It’s hard to get a complete field with Hazy but if the other cards keep the field for Xyz Veil to shine it will.