I haven’t tuned Hohners, Kirill, but have a lot of experience with Yamahas and Suzukis. prodz might have a point that tuning a bit higher might relieve the problem, maybe at 441, which probably would work with bandmates. I was surprised to hear about your experience, though, and my first thought (with hesitation given what the accordion tuner said) was that the problem might be gapping. You can see whether the gaps are noticeably different, and gapping does affect how much of a sound (if any) you get.
The Hohner Student is an inexpensive and cheaply made instrument. I bought one for $25 new and have taken it apart. Its reeds may be of insufficient quality to withstand being all tuned down from 443 to 440. I have tuned several better melodicas, Yamahas and higher end Suzukis (A-34 NS m-32), down to 440 or 441 and have noticed no problem such as you describe. Those melodicas are claimed to have higher quality reeds, and I think you can see that they do, and they don’t corrode so easily.
I don’t think it is unusual, though, for the notes at the low and high ends to be a bit harder to blow (to get the sound you want) than the notes in the middle. I think there is a “sweet range” of a melodica, where it is easiest to play and sounds best, though this varies from one melodica to another and is more noticeable on some melodicas and to some players than to others.