Is there anything preventing us from adding these clause given our contract was awarded using FAR parts 12 & 13?
By definition, a commercial contract is not a construction contract. So mixing supply, commercial and construction clauses would lead you to have you review your scope of work to see which category really be fits bests.
FAR 36.101 – Applicability provides the following guidance:
(a) Construction and architect-engineer contracts are subject to the requirements in other parts of this regulation, which shall be followed when applicable.
(b) When a requirement in this part is inconsistent with a requirement in another part of this regulation, this Part 36 shall take precedence if the acquisition of construction or architect-engineer services is involved.
(c) A contract for both construction and supplies or services shall include --
(1) Clauses applicable to the predominant part of the work (see Subpart 22.4), or
(2) If the contract is divided into parts, the clauses applicable to each portion.
Also note that by adding these construction clause, this could then also require the contract to be subject to the FAR subpart 22.4 Construction Wage Rate Requirements Statute when the contract is greater than $2,000.
The definition of at FAR 2.101 of supplies allows for the basic installation of that supply.
“Supplies” means all property except land or interest in land. It includes (but is not limited to) public works, buildings, and facilities; ships, floating equipment, and vessels of every character, type, and description, together with parts and accessories; aircraft and aircraft parts, accessories, and equipment; machine tools; and the alteration or installation of any of the foregoing.
Assuming your contract and scope is written as one line item, suggest you review your scope of work and determine if it falls primarily in the supply or construction arena. If it is a supply contract, you may just need to modify your scope to cover a few items that were not covered. If it is truly a construction contract, this might be considered an out of scope change and then your options are (depending on the dollar value) doing a J&A for a sole source change or terminating for convenience and starting over.
You could have done separate line items on the contract for construction and supplies (then the appropriate clauses would only apply to the applicable line items) but then that would make it hard to solicit this contract as a commercial item. Also remember if you are performing this as construction and it is over $2,000, then you will also need to include the Construction Wage Rates (formerly Davis Bacon).