Russia's next naval (ASW) helicopter options:
4. New design
Actually strictly speaking the Ka-31 is an AEW helicopter, or radar picket helo, and the Ka-60 is a transport helo, while the Ka-52 is an attack/CAS helo.
The Ka-27 is the current ASW helo, the Ka-29 is the current troop transport helo, and the Ka-52 is the potential new attack/CAS/AShW helo.
The modular Ka-226T helo has huge potential for smaller vessels as it can be used for a wide variety of roles with different modules attached.
Also the Mi-14 can be a good option to take into account in the selection process, surely in the new units there are interesting updates.
The Mi-14 is a very capable land based ASW helicopter...
Actually they would need 2, depending on ship size. Ideally that new Ka-31 replacement we keep hearing about + Ka-60.
The Ka-60 looks interesting, but it is a light 2.5 ton payload helo.
A new replacement for the Helix models would be a good thing, but for the moment on a helicopter carrier like a Mistral or Russian equivalent the mix of Ka-52s for attack and Ka-29s for troop transport would be fine... a few Ka-27s for ASW would be useful too and some lighter helos like Ka-226s would be handy.
Ka-60 will be kinda hard since right now Russia is just getting its production of VK-2500 going for its current helicopters Ka-52 and Mi-28. The current ones used for it are French and based from a contract back in 2011 but obviously that wont work now. So Ka-60 development for military purposes will be pushed back for a couple more years to improve the VK-2500 to Mark III in order to get it powerful enough for the Ka-60.
Not sure what you are smoking but I don't think the new 2,700hp engines for the 10-12 ton attack helos like Mi-28 and Ka-52 would be suitable for a Ka-60 that has a TOW of 6.5 tons... unless you are suggesting a single engined helo... From memory the Ka-60 had engines of about 1,200hp each that were Russian... it is the Ka-226T that has French engines AFAIK.