I have a 12ft Greys Prodigy twin tip rod which comes with two Avon style tip sections:
A 1.5lb test curve tip section for slightly smaller Carp and for Barbel in normal water conditions; plus a 2lb test curve tip section for when I need to be able to handle large Carp or I’m fishing in flood water conditions for Barbel.
This rod also comes in a version with an Avon tip section plus a Quivertip section for those that prefer that combination instead.
Link to rod —>
I caught a 22lb common on my Multi-tip rod when I was targeting Tench using the lighter 1.5lb tip section (see pic) and I regularly catch plenty of Carp up to the 20lb mark on both the 1.5lb tip section and the 2lb tip section and most of these are caught in a weedy lilly strewn estate lake so I don’t think you’d have any problems using the rod at all in the venues that you describe.
I partner this rod with one of my Shimano 55 series reels (the 55 series Is unfortunately no longer sold in the shops but you can find them on eBay) or a Shimano Stradic 4000 GTM RC series reel; but a 6000 reel would also be fine as the 5000 series and 6000 series reels are basically the same size other than their line capacitys.
I also have a few dedicated Carp rods that I often use but these are nowhere near as versatile as my twin tip rod which can be used for a host of other fish from smaller fish right through to decent sized Carp.
Keith