Even with infinite trays, there will be a minimum boil up ratio and reflux ratio. Determine the minimum reflux ratio to meet your specs. Increasing the reflux ratio from the minimum reduces the number of stages needed. Your optimal reflux ratio will be about 1.2 times the minimum reflux ratio. Start with that as a ballpark figure to determine the stages needed. For a more precise optimum, you can then perform a sensitivity analysis around that point to see its effect on capital and operating costs.
Film boiling can be avoided by not having too large a temperature difference at the reboiler. But if the temperature difference is too small, your reboiler will be unreasonably expensive. You may be able to adjust your column pressure so the reboiler process-side temperature is about 50F cooler than the saturated LP steam, but try not to increase the pressure so much that you have to use refrigeration at the condenser.