One should consider the health of the orchid in question to decide to rebloom or not. Blooming takes ALL of the energy and the rest of the orchid gets little or nothing, energy wise.
If the orchid looks stressed and you don't want to risk losing it from reblooming the already present spike, then I would remove the entire spike. If the orchid is strong enough (read: has enough energy stored) then reblooming the old spike is fine. I don't know of a way, other than its general appearance, to determine the energy resources in the plant.
Since cutting a spike off at its base sets to 'bloom clock' to zero, it is reasonable that growing a new one from scratch takes longer. The orchid has to store enough energy to support the blooming cycle and so it doesn't spike until it achieves that energy level.