Great advice, and gratefully received - unfortunately, completely wasted on an impatient and compulsive idiot like myself. So...I now have this:
The Fissure King Mk2
I've recycled a few components from my Krait Mk2, which currently work better than the larger, A-rated, replacements until I can farm a few more engineering mats. It's working really nice at the moment though (I play in Solo, don't forget, otherwise it's a complete and utter re-buy vampire). I like to think of it as my Swiss Army Knife (not the genuine version of course; more like a cheap Chinese knock-off Swiss Army Knife from a market stall).
It feels fine for core mining, and not at all unwieldy, even when maneuvering to blast surface deposits. It's also fine for hanging around nav beacons in Anarchy systems, so long as I pick my targets. It certainly shreds ships faster than my Krait did.
I've still got 280 million cr to spend on upgrades, so I just need to prioritise the modules I upgrade first and make sure I have enough mats to engineer them to a reasonable standard (I'm not fretting over grade 5 on every item to begin with, grade 3 seems to be a significant improvement).
Apologies for the docking computer. It's the only ship I have one on, and there's nothing more enjoyable than spinning your wheels on the way out of a station, but the Anaconda seems wider than the drummer's girlfriend, and I keep jamming it in the letterbox. I also tend to play ED with a guitar on my knee for the boring bits, so the less time I have to spend panicking about docking this barge, the better.
Anyroadup, many thanks for all the advice so far, the community seems infinitely more helpful and flame-free than most of the other games I play. It's great to see the evolution of this game from the very first release, which I bought for the Sinclair Spectrum back in 1984 (when I was 22...that's a depressing thought). It's just as addictive now as it was then.
Time will tell if it was a mistake buying this...