There's no reason at all for choosing a rod with a test curve of more than 2.5lb for playing carp - even huge ones - in the UK. Anything over this is a casting rod. You can't throw a big PVA bag with a 2oz lead in it far unless the rod is powerful enough to do it, but remember that such a rod is always a compromise tool, and will to a greater or lesser extent impede the playing of a big fish.
Casting and fish playing are two totally incompatible actions, so every rod is a compromise. All rods act as a lever of sorts, enabling the line to be held out further from the angler and (through simple mechanical principles) multiplying the effect of hand/arm movement. This leverage helps the angler propel the bait/lead, but works against him when playing a fish. Therefore, unless your particular situation demands a rod capable of throwing a heavy object a long way, stick to the more flexible rods.
That's not to say you must go to extremes - I'm sure Indifferent Crucian would agree that it would be foolhardy to deliberately set out to catch big carp with something as light as a traditional 1.25lb Avon rod - but in reasonably open water such rods are quite capable of landing anything you hook. I have never seen or handled the FM Concept rod, but it sounds perfect for close-range carping in all but the snaggiest spots - and with margin fishing rod power is less significant than line thickness, as near-bank tussles with snag-dwelling carp tend to be a tug of war with the rod held at a low angle and most of the strain being carried on the line. A softer rod can be a help here, as the bend moves down the rod towards the anglers hand and thus imparts less leverage on the arm; it also cushions the hookhold.
Once you start fishing at ranges over forty yards or so, you do need to up the power to 2lb or so, simply to enable more of the length of the rod to be utilised in controlling the fish. Over eighty yards that needs to go up even more, but I have never found it necessary to exceed 2.5lb, even when using small PVA bags. Indeed, the best casting rods I've ever used were Simpson's Jim Gibbinson Eclipses and Daiwa Kevin Nash Amorphous Dictators - both 2.25lb twelve footers.
Sadly, these days it's hard to find carp rods under 2.5lb as the fashion is for ever more powerful tools. Those that are available are generally designated floater rods. If you read between the lines a bit here you can see the absurdity of a marketplace that says you need a 2.25lb rod to fish a floater, yet for a bottom bait you need to crank up to 3.25lb! The carp are the same, so where's the difference? There is none, unless you insist on using huge leads or big PVA bags for everything, or are one of the 0.01% of carp anglers who genuinely need to cast 130 yards plus to reach the fish.