Hit Dice for Homunculi

[Phylion]

For the Artificer's Craft Homunculus class feature, it states that the Hit Dice of a Homunculus may not exceed the Level of the Artificer -2. Is it possible to still create a Homunculus with a larger number of Hit Dice than that by using the normal rules for constructing constructs, by paying the 5000gp per Hit Die? For example, say I am a sixth level Artificer, and I have Craft Magic Arms and Armor, Craft Wondrous Item, and Craft Construct. Although I am not able to advance a Homunculus to 6 Hit Dice with Craft Homunculus, could I still make a six Hit Die Iron Defender with the Craft Construct feat?

EDIT: And it still benefits from Improved Homunculus, right?