Lots of useful information here mucker. Having had 50 years of experience playing vinyl with turntables and cartridges of all types since the 1960s I can say this:
#1 Moving Coil cartridges have clear advantages over moving magnets if you can buck up to pay for the good ones. On a limited budget, you likely might have better sound from a higher end moving magnet or moving iron cartridge than a lower end moving coil.
#2 The phono stage upgrade is likely to give you a very worthwhile improvement in sound for a relatively small outlay, even with your currrent cartidges.
#3 The best moving coil cartridges are generally lower output. When you get into those cartridges, set up and impedance loading are important and you need a much better phono preamp to allow you to do this.
#4 In my experience different Cartridges Brands have different house sounds and sonic signatures and you need to read reviews to get a sense of where to go with that. For example, with low output moving coils, the Lyra brand tend towards clear, and a bit analytical. Koetsu and Benz, tends to sound a bit warmer and more forgiving. In general though, most moving magnets tend towards a warmer sound. Going up the Sumiko like you will get more clarity for sure but not necessarily more warmth.
#5 Lots of people buy a cartridge only to find the cartridge is not what they expected or wanted from a sonic profile point of view, wait until they break in ( 50-100 hours) and when they don’t change enough to their liking, list them for sale. Consider buying a lightly used cartridge....if it doesn’t live up to your expectations you can sell it for what you paid for it.
#6 With added detail and clarity from moving coils, flaws in vinyl are often more apparent as well. So best if your record collection is in very good condition.