Exquisite abominations: I want it good, cheap and fast!

I'd suggest making it more of a card-driven game, with mechanics as well as components. Make the board out of a grid of cards dealt onto the play surface, like 3x3 or something of that nature, and a card on an outer space to indicate that player's impregnable "home base." Each card here represents a different region the players can visit and/or have their creations battle one another.

The body parts can be laid out in front of the players: torso at center, head at the top, arms on either side, and two legs - or one card representing both legs on a bipedal, humanoid creature - below. You likely had this in mind already but this might clarify what I'd been describing. Body parts can be replaced as needed by taking out a card and putting another in its place. If there are augmentations to certain body parts (like a cybernetic eye or armored greaves for the legs, for example), simply "shingle" the cards so they overlap but crucial information can be seen underneath.

To keep things simple, use counters/pawns for each player, a deck of cards for the board and body parts, and either play money or a tracking card for each player to deal with currency.

I'd imagine that a "king of the hill" mechanic, similar to King of Tokyo or Talisman, might serve you well. The center card of the play area is the hill, and if a player occupies that space long enough, they win the game.

Simplify combat: add attack/defense values to the body part cards. When two players occupy the same space, combat occurs. The player who has the lower attack value is forced to move to a different space. If players tie, they are both forced to a different space. It may be that a player may be forced back to their home base, but at least none of their opponents can invade there.

Best of success with this! I wish I had something like this in Spanish class decades ago. :)

What about using cards which have different body parts or limbs, but having a slightly carcassonne-like element, so you can make a monster with a loooong torso consisting of multiple cards (and thus able to have many arms for more attacks) but more difficult to complete (because you need to have a completed monster to fight), or a smaller monster with the minimal number of cards, which fights less well, but is easier to make. I think you'd have to allow multiple monsters under construction per player if this were to work well, though. Otherwise maybe you can modify your monster once it is complete, but it uses a turn during which the monster is out of action.

Extended arms could increase attack range, a bigger torso could increase hitpoints but make the monster easier to hit, longer legs mean it runs faster, and so on.
I am tempted to try to make a game along these lines, but with a science-fiction vehicle theme - probably inspired by those toys with the different mechanical arms and legs and tracks and stuff that connect together to make mech-like or tank-like futuristic vehicles.