The problem you're running into is almost definitely the static pressure rating of a biscuit fan (PC case fan). It's incredibly low. All you need to do (probably) is add a blower (aka squirrel cage fan) to your original intake adapter and let it handle increasing the flow rate and most of the reduction. Then model and print an adapter that fits the rectangular exhaust aperture of the fan and your 15mm ID tubing. Keep the tubing as short as possible, as the longer the air path, the higher the static pressure.
I'd also suggest you use a beefier blower than the one that's probably cooling your nozzle(s). By a lot. You probably want a 12v blower with a 60 to 80mm diameter housing, by about 40mm thick. That said, even two fans of the same size, voltage, and wattage can have wildly different static pressure ratings. Virtually every fan manufacturer will give you the static pressure rating of any fan you buy/inquire about, even if it's not listed in the specs. Most small (<1A) 12v fans don't list static pressure ratings, but you can usually find out via an email or even posting a question on an Amazon listing, if the manufacturer or seller are attentive.
You also don't want your adapter to use a funnel shape internally, as that increases pressure. Instead, you want it to transition from rectangular to round, and then hit a flat wall inside, with the appropriate diameter aperture inside of it, as that will increase your flow rate, instead of increasing your flow pressure, thus reducing the restriction while removing a similar amount of heat as your unrestricted biscuit fan did before.
Finally, while there's lots of fluid dynamics simulation you could do to optimize the exact length of the adapter before you hit the reducing aperture, IIRC there's a rule of thumb to use, or you can just assume that you want a fairly short chamber, that allows enough space for a fairly static air mass to form around the aperture, with a smooth laminar flow from the wall where it becomes round to the aperture where the high speed flow exits, and then experiment a bit. I'm thinking the golden ratio relative to the reduction in radius is probably a good place to start, but I really don't recall offhand, and that could be wildly off.