Tweening model in relative space?

Yeppers, of course there is. Get the player's current position like this:

local CFrame = Player.Character.PrimaryPart.CFrame;

We use CFrame in order to maintain rotation. Just think of CFrame as a Vector3 with rotation properties.

We then add the CFrame's lookvector (multiplied by a constant, which is the distance) with the CFrame's current position. The LookVector is a Vector3 value (hence Vector), which means it can be added to a CFrame value, like this:

local Formula = (CFrame.LookVector * Constant) + CFrame;

Now, you can utilize TweenService to make the tween. We don't have to worry about using :ToEulerAnglesXYZ() here because we're maintaining the rotation values by adding a Vector3 to a CFrame.

TweenService:Create(Player.Character.PrimaryPart, TweenInfo.new(0.25), {CFrame = Formula});