We analyze multi-user fluid antenna systems with continuous positioning over a track of length L under a spatial correlation model, where exact performance distributions become analytically intractable. We develop a level-crossing-rate (LCR) framework that yields asymptotically exact approximations and tight bounds for the cumulative distribution function (cdf) of the optimized metric S* = sup_{0 <= l <= L}, where S(l) denotes the performance metric at antenna position l. For a single fluid antenna, we characterize the cdfs of signal-to-noise ratio (SNR), signal-to interference ratio (SIR) and signal-to-interference-plus-noise ratio (SINR) under Rayleigh fading and extend the approach to Ricean desired channels. We further treat two multi-antenna receiver layouts with maximum-ratio combining: (i) a fluid antenna with a fixed antenna and (ii) a two-element moving array, deriving new LCR results for the practically important case where array-element correlation and positional correlation are inherently coupled. The analysis provides actionable insights: high-threshold tail probabilities scale linearly with L, we derive the required L to neutralize a co-channel interferer, and we show that about one wavelength of movement can reduce outage by three orders of magnitude. Monte Carlo results validate the accuracy across the considered scenarios and regimes.