[Solved] How do you make part face snapping?

So I have this extremely simple part (and model) placing script thats skeleton looks something like this...

local player = game.Players.LocalPlayer
local mouse = player:GetMouse()

local model = game.ServerStorage.Model

local build = false

function startBuilding()
	build = true
	local obj = model:Clone()
	while build do
		wait()
		model:SetPrimaryPartCFrame(CFrame.new(mouse.Hit.) * whatever_rotation_angle)
	end
end

mouse.Button1Down:Connect(function()
	if not building then
		startBuilding()
	else
		building = false
	end
end)

Very simple, but the issue with it is that when the mouse.Target has an object in it, the mouse.Hit.p gets a bit skewed and ends up placing the model a bit higher up and inside of the mouse's target.

Example 1

Example 2

The desired behavior I want is for when mouse.Target has an Instance, then snap to the mouse.TargetSurface regardless of the rotation of the model.

How would I offset the model so that it sort of snaps to the face of the mouse's target?

Edit: I was able to get the height to snap in this example, but I still don't know how to snap the X and Z according to the side face.

Height Snapping Example

Ended up doing it by taking the mouse.TargetSurface values and specifically offsetting the model to whatever the surface was.

Solution