In fact, it was based on Bazalt. Here is what the "Naval Institute Guide to World Naval Weapons Systems Fifth Edition (2006-2007)" says about it:
" A successor P-1000/3M70 (Vulkan, which is SS-N-12 Mod 2) is largely a Bazalt airframe with new electronics. The designation suggests a much improved P-500, just as Link 22 is an improved replacement for Link 11. Reportedly, its warhead was armoured (with Titanium) against CIWS rounds, and some steel parts were replaced by titanium to cut weight. It had a more powerful engine and a more powerful booster; better fuel economy extended range range to 700 km.
Reported details;
launch weight 4.5 tons with 1000 kg warhead
speed mach 2.3
length 11.6 metres
minimum flight atitude 40 metres
Reportedly, development was approved by the Council of Ministers on May 15, 1979; land trials began in July, 1982, followed by a submarine trial, from an Echo II submarine, on December 22, 1983. Although the five Echo II submarines armed with this weapon have been discarded, it survives aboard Slava class cruisers, having replaced Bazalt."
Hope this helps. Although a little pricey, fifth edition has lots of interesting info on Soviet/Russian stuff. I found my copy on for half price with a damaged cover but otherwise in excellent condition, and the rest is history.