Greetings from the land of the Maple Leaf
If you’re looking to put down an opaque white in one hit, the size of screen mesh will play a huge part. You would probably want a coarser mesh than for ‘normal’ printing. Also, assuming you’re using plastisols, there can be quite a difference between brands – try looking for ‘Super Opaque’ on the label. Also, if you’re hand printing these, two or more strokes of the squeegee is usual.
The goo you’re finding on the stencil when washing out is almost certainly a result of underexposure. You should try a simple exposure test – use any piece of film positive you have to hand and mask all but a fifth of it with a piece of black paper or thin card. Expose the stencil for a minute, uncover another fifth, expose another minute, and so on. Expose the last one for your ‘normal ‘exposure time. You’ll end up with a stencil that has five bands -the last one having been exposed for your normal time, the next +1 minute, the next band +2 minutes, then +3 minutes and so on. Wash it out and determine which band gives you what you need. You should then have an indication as to what is the correct exposure time for your particular set-up.
Hope this is helpful!
Graham.