I agree with Ziz that demand is different at different price. As long as demand has a high elasticity to price, there will generally be a higher demand at lower price. Interpreting it at an interval is not very realistic and misleading.
On the freedom to adjust price though, I will have to go with you. You're right that the freedom to adjust price will lead to this 1 gil undercutting which makes the journey to equilibrium slower because the incentives are not there to adjust further down. With restrictions such as tax to adjustments, there is an incentive to post at a lower price that will have a higher probability to sell since you no longer have the freedom to readjust the price freely.

However, this also depends on the size and activity of the market. Given sufficient market participants, prices will hit equilibrium quicker with or without freedom to adjust price. At a large market like this, restricting freedom to adjust price decreases the market efficiency because it introduces another economic phenomena called sticky price. That means that when the equilibrium shifts, it will take longer for the price to adjust to reflect that because there is now a cost associated with price adjustment.

So, I believe your idea would work only in a small market...but not advisable for a large market.