Hello Beezer, I would hate for you to drill a hole in your melodica, but it sounds like you may not have enough volume from the melodica where you are placing the gooseneck Mic, causing you to have to raise the volume to much on your amplifier. I have several melodicas that have this same issue. Example: I have a Hohner profession 36 that has sound hole/slots where the sound emits from the Melodica and thats where I place my Gooseneck giving me plenty of headroom for the amplifier and I get plenty of melodica volume through my amplifier. Now I have a Hohner Piano 36 that does not have any sound holes and I have to place the gooseneck over the keyboard so I get a lot more indirect sound from the clanking of the keyboard and room sound that feeds back into the amplifier causing feedback, this is the same for my clavietta. What I did for the clavietta was to remove the metal cover to check if I could get a more direct sound. Once I did this I was able to raise the volume about 30% more on my amplifier before feedback started. Since I have several end caps for the clavietta, I drill a hole and taped the gooseneck to the metal cover in the inside and now I can get a lot more melodica volume to send to the amplifier and since the goose neck is covered from the room sound it removed the feedback until I get very loud with the melodica. Some melodicas are easier than others and some just do not work due to noise where you can pick up a lot of clankng from the keys. You mentioned in your post that you used a DI with a parametric equalizer. I use a SanAmp Paradriver DI that works great to remove frequency that cause feedback. When using a parametric equalizer the trick is to start with an even EQ set up. With the mid range cut feature, find the frequency that is causing the feedback and roll that frequency back as needed. I actually use this a lot as all melodicas produce different harmonics so you have to tweak the mid as needed for different melodicas. Lastly for the pickup issue, your amplifier set up needs to be tweaked in the same manor, usually I first cut all the mid off and raise it slowly keeping the base and treble about 1/2. And remember if you are too close to the amplifier it will feedback by nature. I have my amplifiers when practicing approx. 7-10 feet and I can hear the melodica with its effects clearly with plenty of volume. My indicator is my wife usually telling me to lower it.
A little on the effect pedals.
It is true that many pedals will not work with the melodica easily, the reason for that is that you no not have a strong enough signal from the melodica to generate the processors to function. Example: The Hammond 44 is a lot better for effects pedals than the Hammond Hyper, simply because of the tone differences that each produce. What I have done to help this situation is to use a buffer pedal to push the signal about 5db before the effect pedal I want to feed, Big difference, I have done this going directly to the amplifier Example: Melodica to buffer then amplifier. I could not get a strong enough signal to a chorus pedal to work, but with the buffer added the processors get plenty of signal and the effect is clearly heard. I have found that combination pedalboards that features different effects on one unit does not work well with melodica. I feel that individual pedals are best for the melodica. I went through several chorus pedals before I found the one that worked best for the “melodica” I wanted to use it on. One pedal may or may not work well with all your melodicas. Many stores have a “No Questions Asked” return policy on pedals, that allow you to take the pedal home and try it and return the pedal if it does not work as expected, allowing you to try a different one. Unfortunately there are no reviews on effect pedals with melodicas that you will find on line that can help you decide, but there are plenty of videos of pedals with guitar and keyboards that can demonstrate the effect that can help you decide if you like the effect for your melodica or not.
I hope this helps you a bit
Monsters of Melodica