Filling the reservoir is not the same as filling the radiator. When the bike is cold you should fill the radiator with a 50/50 mix of antifreeze and water. On some of my bikes there is also a bleeder screw that you loosen to allow trapped air bubbles out, if I had a Reflex I would know if it had one and where it is.
I very much hope that your engine did not get too hot and/or damage the head gasket.
If on the outside chance you need a head gasket NEVER use the Chinese gaskets, you will just have to do the job twice, stick with OEM Honda parts as the quality is much better, I learned this the hard way. My Elite 250 has a similar engine ( however slightly more vertical than yours) and I will NEVER again use Chinese knock off parts.
Hope you get it up and scooting soon and easily.
By the way, the float is inside the carburetor and controls the amount of fuel inside the carburetor, it has no relationship to the cooling system.
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