A Schoeps microphone of the Colette serie consists in a body containing the electronics: CMC5 or CMC6 (minor difference), and a cap: MK 2, MK21, MK4 and others with different frequency responses and directivities. They can be found at a much lower cost than previously since they have been recently available from Internet dealers, but it is at least two times more expensive than the Neumann KM 184.
One year ago, I could compare a pair of Schoeps with two types of caps with my Oktavas. I could hear that there was a difference but was not ready to pay 10 times the price of the Oktavas for it.
The most famous model from DPA for classical music recording is the DPA 4006: it is an omni directional small diaphragm condenser. Also available from Internet dealers but it is still more expensive than the Schoeps, about three times the Neumann KM 184.
Anyway, I think that your choice for small diaphragm rather than large one is the good one: easier placement, more natural sound. And most often used today for classical music recording. In good acoustics, omni microphones are most often preferred to cardioid ones by professional sound engineers. For home recording, cardioid may be better. For sure the KM 184 is not a wrong choice, despite some polemics whether it is as good as the KM 84, the now mythic microphone that it is replacing. (You can read about that on the Neumann forum.)
I cannot propose you a better alternative for the same budget because I am only an amateur and do'nt have the KM 184s. In my previous post, I was just suggesting that your comparison demonstrated that for a important increase of price, there is a significant improvement of the sound. Which is fortunate but not a priori so obvious.
Here attached a document in German that I found on the Neumann forum about several microphones configurations for classical piano recording. It is of minor interest for home recording, but interesting with respect to the diversity of the microphones and their placement.
Edit: attachments removed.