Have you considered using a save and continue formula button, and naming it something like "Get Price"?
I tried to recreate the issue on my account. If I go to new record and then Save and keep working, it will do that, but the Save button reverts to regular "Save". If I click the dropdown, I can select Save and keep working. If I do that, it will then stay there. I had the same issue that after the first save, the "Save and next" button just disappears.
I didn't have the save going to a new form issue. Are you reaching the form from a dashboard or is it embedded somewhere?