Custom ductwork mixing box vs manufacturer accessory

It is difficult to properly cool two spaces with vastly different heat loads and only one thermostat.

Assuming typical computers and monitors and two users, you probably have about a kilowatt of heating or 3400 BTUs per hour.

Rather than run ducts, have you considered a dedicated cooling unit for your office? You can go with a small window unit. Even the smallest one is 5000 BTU and only uses about 500 watts when running. That's just a few pennies per hour and even that is offset by the reduction in load on the main unit. With the thermostat in the same room, its load response will be much better and the temperature extremes you have been suffering with will be eliminated. Plus you can turn it off when no one is there and save energy that way.

Lately my thinking is that ducts are basically parasites and efficiency goes up when the heater/cooler is in the same room as the load. In the past, the equipment cost was lower with a shared unit but operating costs (energy) have gone up a lot (and will continue to go up) and that could change the equation on selecting shared or dedicated equipment. Comfort will always be superior with dedicated equipment.

You need to know how to calculate the required CFM - cubic feet per minute - that your ductwork will allow. On a room per room basis you need to determine how much air flow is needed, how large the vent needs to be, and thus how large of a duct you require. Then you need to determine how large of a trunk you require and at what points you need to reduce it after branching off legs from the trunk.

Finally you need to also know where to position the return air and how large it needs to be, in order to support the output from your HVAC.

I don't know how to calculate those things - I just know that's what you need to know.