1. Small apertures' one advantage is their being able to see a large amount of the sky at once. For any coherent aperture the larger it's span in a direction the smaller the beam pattern is in the perpendicular direction upon the sky. The bigger your collector the smaller your beamwidth the less you can see at once. Big dishes have small FOV and aren't good for monitoring the entire sky.
There are ways of getting around this: physically scanning the big antenna, multi-apertures for receive across the focal plane, or by abandoning actual imaging and measuring the correlations between arrays of lower gain (smaller) apertures.
But the best way (if the signal is loud enough) is just to have a smaller aperture. Real science monitoring for transient radio signals can and is being done with literally just using the feedhorn from a large dish by itself (with some precise clocks, expensive lna, receiver, and time stamping) to detect FRB (and other high power transients),
https://arxiv.org/abs/2001.05077 STARE2: Detecting Fast Radio Bursts in the Milky Way
Multiple stare2 type instruments distributed around the world are likely to do real radio astronomy in the near'ish future. This is amateur scale possible. In the "Completely Hackable Amateur Radio Telescope" they're using a pyramidal dish because it's easier to construct but for trying to contribute to "real" radio astronomy you'd want a choke ring feed horn or at the very least a conical horn. The idea is to minimize sidelobes which otherwise prevent you from knowing for sure the signal you received came from the direction the horn is pointing.
2. Another low hanging amateur accessible "real science" is actually doing something when you're receiving solar radio emissions. Calculate the velocity of a CME shock by the frequency drift as it travels upwards through decreasing magnetic field. Or even more audacious, use a hackrf (or ettus usrp b200 or something) to frequency hop at 8 GH/s over a few hundred MHz bandwidth and record the fine structure present at milli and microsecond timescales precent in many types of solar radio bursts. Things like spectrogram zebra patterns and fiber bursts and other unexplained highly coherent fine timescale patterns which still lack accepted physical explaination today. Particularly in that their very short timescales indicate the emission regions have to be only ~a handful of kilometers in scale but outshine the rest of the sun. Whatever "small" solar features are making these short intense radio emissions are open to even amateur interpretation at this point.