What year is your Wing ???
The system needs pressure tested first. Any leaks must be corrected prior to installing new anti-freeze. The coolant Honda requires uses chemicals, instead of silicate, to help keep the system clean. If there are still leaks, those cleaning chemicals will often make any leaks worst. Also, the system must hold pressure for proper protection on hotter days, so the cap needs pressure tested too. If yours cap is original, and your Wing is a 2002, it's likely been bad for a long time.
The reservoir needs removed, cleaned, and inspected. The tube, level that the reservoir hose fits into might be cracked, as well as the to reservoir hoses that route to it. Check for cracks on both ends. Remove the one under the cap and look.
If you still have problems, the shelter might need removed, and the radiators too. Cleaning them when on the bike may not be good enough. When I have those off, I use a a/c coil cleaner from Home Dept. I spray one side at a time allowing the foam to soak in, then flip them and spray again. After about 15mins of sitting, I use one of those pointed water nozzles to rinse with. Be careful not to damage any grids with the water pressure. If you have anything blocking airflow in/out of the rads, you may need to permanently remove it.
Certainly changing it helps, but it really it needs done every 2yrs/24k whichever comes first as Honda requires for a properly maintained Wing. If not, the cooling jackets on the cylinder walls get coated with what looks like a white porous powder that restricts heat flow into the coolant. The 2nd picture shows a healthy water jacket.