There are two earlier base designs shown in catalog illustrations, which have never shown up in reality. The "rocket" uses a glass base shaped like yours, save that the glass is gripped by four fin-like legs splayed outward, which are connected to the metal tray below. The "pineapple" is again, similar to yours but the difference lies in the pineapple-shaped glass as opposed to a cone-on-cone shape. Both had textured glass and came in three colors: yellow, red, and green, to match champagne mist, red/clear, and green/blue colors, respectively.
Your base WAS frosted originally. This type had a frosted faux finish applied to the glass, which almost always flaked off with age. And yes, a glass shop can probably sandblast the glass to a nice frosted effect, which I don't believe will devalue the lamp. Use a tealight in a tin cup for heat.
As far as I know, all Continentals originally came with a "frosted" coating. The coating is quite delicate and prone to flaking off.
The early versions of the lamp may simply be an artist's renditioning of the lamp. No 4-legged or "pineapple" Continentals have yet to be seen, although they may exist.
Note the artist's renditioning of the Continental in the following Lava brochure from 1966:
Also, here is some information on the "happy ocassion" globes next to an ad for the "Savoy" from the same 1966 brochure. Note the different hole pattern on the metal part of the Savoy model, compared to the Continental models.