How do you move a model using the TweenService?

Thanks for checking out my question!

I was wondering how I can move a model smoothly when using ":SetPrimaryPartCFrame()" on the model.

I'd like to use the TweenService to achieve this effect. Is there maybe a better way to move it than SetPrimaryPartCFrame(), like a value, so I can use the TweenService?

On a side note, can I move it without a primary part? I don't really want to put a middle part inside all the models I'll be using. I know model:MoveTo() exists but this causes it to always be on top, which isn't what I want because it also glitches out when it's at your player.

This is my code:

wait(2);

local previewItem = game.ReplicatedStorage["Wood Crate"]:Clone();
previewItem.Parent = workspace;

local exclusions = {};

for index, descendant in pairs(previewItem:GetDescendants()) do
    if descendant.ClassName == "Part" then
        descendant.Transparency = 0.5;
        descendant.CanCollide = false;
        descendant.Anchored = true;
        table.insert(exclusions, descendant);
    end;
end;

table.foreach(game.Players.LocalPlayer.Character:GetDescendants(), function(i, obj)
    if obj.ClassName == "Part" or obj.ClassName == "MeshPart" or obj.ClassName == "Hat" then
        table.insert(exclusions, obj);
    end
end);

local mouse = game.Players.LocalPlayer:GetMouse();
local camera = game.Workspace.CurrentCamera;

function round(n)
    return math.floor(n + .5)
end

mouse.Move:Connect(function()
    local unitRay = camera:ScreenPointToRay(mouse.X, mouse.Y);
    local ray = Ray.new(unitRay.Origin, unitRay.Direction * 500);

    local part, pos = workspace:FindPartOnRayWithIgnoreList(ray, exclusions);

    if part then
        previewItem:SetPrimaryPartCFrame(CFrame.new(Vector3.new(round(pos.X), round(pos.Y + (previewItem:GetExtentsSize().Y / 2)), round(pos.Z))));
    end;
end);

If any part of the code can be more efficient, like the exclusions, please let me know too :)

tldr; I want a model to follow the mouse on a grid with raycasting, smoothly, and preferrably without setting the PrimaryPart. How?