I'm not sure if iGPU's are typically used for transcoding, which may be part of why you're having difficulty finding solutions.
As for re-encoding H264 into H265, increased file size is common. Encoding from source for the first time into H265 will lower file sizes, but if you're re-encoding something you're almost always going to lose data while increasing file size, especially on hardware encoders due to the methods and time it takes.
Basically, try your hand at Very Slow software encoding. Wait a day. This H265 file will likely be smaller than the Hardware Encodes of the same thing.