Hilltop castle, 50ft walls, 10ft thick, garrisoned by 350 men. Foundations of solid stone 15ft deep.
Also has a 200ft Watch tower on the east side, and single foot thick iron gates on the west side.
I assume this single wall goes all the way around the hilltop? Sounds more like an upgraded version of a standard motte & bailey.
I'm going to take the historically accurate route then. An army... no, more like a small unit of a larger army, of around... eight-hundred or more men. (Normal armies were usually in the tens-of-thousands which were broken up into units for easier management. Or something.)
Firstly, I levy the locals into my army, by sword-point if needed, and procure [i\]all[/i] of their resources. Food, timber, metals, whores, whatever. Anything to keep up morale, feed the soldiers and equip them.
After preparing suffiecient siege defenses. I encircle the country-side around the hilltop, cut-off supplies and throw the poorly equipped local peasants at the enemy. I immediately throw them back if they retreat. Should they be persistent in the retreating, I hang them.
I'm not feeding the peasants anyway, and i'm only giving them farm-equipment and easily salvaged siege equipment, so I shouldn't lose substantial resources.
When I run out of peasants, I remain in my same position.
Should the enemy sally forth, they will be forced to do battle running downhill and across a significant expanse of land to meet my own heavily fortified forces and will not have the previous comfort of 50ft walls.
If I am successful, I pillage whatever resources necessary, occupy the castle until reinforcements arrive, and continue onwards.
If that battle happens to sway in the enemies favor (Possible, as my forces will be quite spread thin around the castle) I will order a tacticl retreat.
I can return later however.
The enemy has recently lost [i\]all[/i] of their local peasantry, most of them killew by their protector's own hands no less.
Anyway, I don't think you've explained the specs of the battle enough. This is all based on me guessing outcomes.