If what you actually want is urgency: a reason to act today rather than bookmark it, there are ways to get that without touching the price.
A closing window on something scarce. The first fifty get onboarding help from you personally. That is genuinely limited, genuinely valuable, and costs you time rather than margin.
Founding customer status with something attached - a say in the roadmap, a mention on the site, direct access to you. People value being early and it is free.
A price rise announced in advance. The price goes up on a date, and early buyers keep the current one. This creates urgency and it does the opposite of anchoring low, because it establishes that the price goes up over time.
That last one is the shape I would use, and it has a bonus: it makes the eventual increase a thing you have already announced rather than a surprise, which is most of what makes raising prices difficult.
And one practical note whatever you choose: write down what happens to the launch cohort before you launch. When they renew, at what price, and what you will say. People discount without deciding that, and the decision then gets made in a year by whichever email is most uncomfortable to send.