Something I picked up from freeflighters a few years ago about getting clear dope onto silk (I have used this technique very successfully with silkspan, too) solves all the drip-through worries of the first few coats of dope on silk/silkspan:
Get a roll of toilet paper. Keep it handy. Now, starting a an edge somewhere, like center of the wing, or the fuselage joint if the wing is already fitted, lay your toilet paper strip 3-4 sheets long down on the wing. Get your brush well loaded with dope, and apply it to the toilet paper, getting a good wet patch on the toilet paper the whole width of the paper. Drag the paper along the wing, the dope will transfer from toilet paper to silkspan. Keep dragging and wetting the toilet paper, keeping that wet spot in complete contact with the wing. Work your way to the tip, lay the paper down next to the doped area, and do it again. If the paper tears or gets worn, ditch it for a new piece and start again. Using this technique, I never have had a drip go through silk or silkspan, and I have a nice yellow-silk-covered Waco cabin biplane as evidence.
This technique should be done for the first couple of coats, then you can brush on the remaining coats you wish once the pores are sealed up and no drip-through can happen.