About the risk of feeding hot signal into the Zoom: if I recall fine, the H4n doesn't accept signals as hot as the improved H5 and H6. I second the advice not to spend so much money trying to improve the H4n, but if you go that route better check the overload risk anyway....
I own a Zoom H6 which I like (flexibility, 6 channels, interchangeable capsule for point and shoot). In close- medium miking, both with stock capsules and external mics I can pull good noise free recordings, but it's preamps get a bit noisy going beyond 6/10 of the dial range. So absolutely usable and flexible but with some limitations in terms of distance/mic sensitivity/music genre. Plugging in my Naiant Littlebox gives better results sound wise, but not really an appreciable upgrade in noise performance. Tried to plug my Audient evo4 interface out to Zoom input and I can get an audible less noise. The EIN of my interface ( -129db) is a lot better than -120db on the Zoom so, still not bypassing the recorder's preamps there is still a plus. BUT I need to engage the -20 pad on the recorder, otherwise the overload risk is there. Don't know if the H4n has an attenuation pad.
A viable solution if you want to keep the H4n could be a couple of fethead phantom inline preamps. The Phantom version passes power to the mics after keeping a part for self powering and it should give a 18 db boost with less gain needed from the recorder. There is a video by Curtis Judd on YouTube testing these gadget with H4n and the improvement sounds substantial, as shown also in a DAW. Yet it is a matter of thinking if spending 150 bucks for these....however the improvement with the old H4n is there, more questionable with better stock preamps as, while very convenient, unobtrusive and cable free it is always a preamp feeding another preamp. Berliner 33 had a - 40 db sensitivity so you'll end up turning them into a -22 mic; maybe still too hot?
I also would sell the H4n....