Hi Jeremy,
If you’re up for it, yes, a refractory mortar liner would help, though I’d look into insulating castable for that purpose. @BrickWood would know more about that than me, but the caution is that you need first to scrub clean any surfaces on which you plan to apply it, and I’d also use a bonding medium. If you go that route, plan on a thorough fire-curing cycle over a period of about a week or else it will crack and come down into your food.
And yes, you could leave the hearth in place and step up over it. If you do that, I’d recommend a layer of sand for leveling, then a layer of facing brick (cut your bricks lengthwise) laid in a herringbone pattern. To make that work, you’ll want to add a “lip” across the entrance so you have an enclosure for the sand and firebrick.
The instructions for the various ovens include how to set up and lay the hearth brick, and why you’d want to do them in a herringbone pattern rather than perpendicular. The reasons you’d want to lay them over sand and not mortar them in are: 1. If a brick ever heaves (which happens both to mortared and loose brick) it won’t catch the lip of your peel—not as big a deal with your design but still a consideration; 2. If a brick ever breaks you just lift it out and replace it.
It sounds like you’ve got this, Jeremy. Hope this helps!