Your condo violates Code and is unsafe, and your HOA consists of idiots
First off -- your condo's existing setup, with a recirculating hood over a domestic gas appliance, is quite clearly a Code violation and a flagrant safety hazard, as IFGC 503.3 strictly prohibits the recirculation of gas appliance exhaust due to the unacceptable CO buildup that would otherwise occur:
503.3 Design and construction Venting systems shall be designed and constructed so as to convey all flue and vent gases to the outdoors.
Second, that ceiling exhaust in the laundry room likely was installed to service the dwelling unit -- you'd need to replace that ventilation system in order to reuse the existing exterior penetration for the range hood duct, and that leaves you back where you started.
However, if you can have an engineer analyze your ventilation situation as per Chapter 4 of the IMC and determine that the vent fan in the laundry room is indeed not necessary to provide Code-compliant ventilation to the dwelling unit as a whole, then you can disconnect the ductwork from the laundry room vent fan and reuse that penetration for the range hood, provided that the duct meets the conditions given in IMC 505.1 for domestic range hood ducts:
505.1 Domestic systems Where domestic range hoods and domestic appliances equipped with downdraft exhaust are located within dwelling units, such hoods and appliances shall discharge to the outdoors through sheet metal ducts constructed of galvanized steel, stainless steel, aluminum or copper. Such ducts shall have smooth inner walls, shall be air tight, shall be equipped with a backdraft damper, and shall be independent of all other exhaust systems.