# Running several MCMC chains after convergence?

I am running a MCMC Gibbs sampler for a computationally expensive model. It takes ~12 hours to obtain 1000 iterations of this MCMC sampler. I have tested the sampler, and I found that the chain seems to have converged after 2000 iterations (1 day). So, I am planning to use the last point of this chain as a new initial point in order to run 10 chains in parallel (using different seeds) with this initial point, in order to reduce the running time. So I will end up with 10,000 posterior samples in a tenth of the time.

Is this a valid approach?

I would rather not suggest this course of action since, all chains starting from the very same point, $$X^{(2000)}$$ say, these chains need run long enough to cancel the dependence on that starting point and recover simulations from the target. For instance, if one removes some burnin part (20%? 50%?) from all 10 parallel chains, this would come closer to a set of 10 independent MCMC samples run under the stationary distribution. But