Very happy with the thing. I only wish: XY was less choppy
Not sure what you mean by "choppy" - the movement or the rendering.
I don't have a SDS1202X-E at hand right now, but:
If it's anything like the more advanced models, then the movement should be totally smooth at least with reasonable record lengths <1 Mpts. Likewise, the rendering should be quite nice because of the high waveform update rate and intensity grading. Of course, it is still 8 bits, especially noticable in XY-mode, where a LSB corresponds to two pixels on the screen. An SDS2000X Plus in 10 bit mode does a much better job in this regard.
... the FFT included phase information instead of just magnitude,
At least on an SDS2000X it does; just download the FFT data from the scope, it contains everything.
there was a Gaussian window,
Yes ... and Kaiser, Blackman-Harris, Barlett ...
Remember, this i just an 8-bit scope. I dare to say that Flattop and Blackman is all you need in practice.
could compute spectra of C1 and C2 simultaneously,
This would require two math channels like an SDS2000X Plus. Maybe too much asked for a bottom of the barrel entry level model?
bandpass filter
Since Siglent offers decent math - not just on heavily decimated data, or even only screen data - this takes quite some resources, available in higher end models only.
+mix+downconvert settings for FFT.
Very interesting request. I've demonstrated something similar on an SDS2000X HD, using the formula editor. It worked well on a 12-bit device, but not with just 8 bits.
https://www.eevblog.com/forum/testgear/siglent-sds2000x-hd-12bit-(published-for-chinese-domestic-market-only)/msg4320658/#msg4320658