You’re already in a really good place gear-wise, so it makes sense that you’ve hit that “what’s next?” phase. I’ve used (and heard a lot of) the CA-11s, and they punch way above their price. The jump from CA to Neumann is massive — but so is the price, unfortunately.
A few thoughts that might help:
Sound Professionals vs Church Audio
The SoundProfessional cardioids are generally a step up from the CA-11s, but it’s more of a refinement than a night-and-day difference. You’ll get a slightly cleaner top end and a bit better off-axis rejection, but it won’t feel like going from “prosumer” to “studio” level. More like polishing what you already have.
Rode NT5
The NT5s are actually very solid. They don’t show up as much in taper circles because they’re bulkier and harder to stealth, not because they sound bad. Sonically, they’re closer to true small-diaphragm condensers like the KM184s than your current mics. If you don’t need ultra-stealth, they’re worth serious consideration.
Really good “middle ground” mics to look at
If you want that in-between Neumann and ChurchAudio territory, these are often sweet spots:
Line Audio CM4 – probably the best bang-for-buck option right now
Oktava MK-012 (with cardioid caps) – very musical and natural sounding
Audio-Technica AT4021 or AT4041 – clean, reliable, great value used
sE Electronics sE7 – underrated and inexpensive for how good they sound
These are all noticeably more “real mic” sounding than CA-11s but far more affordable than KM184s.
Recorder pairing with Zoom F3
The F3 is a fantastic choice. Its 32-bit float paired with better mics is a very real upgrade path. You’d immediately hear the difference just from improved transient detail and stereo image.