Paul,
Some info I have found....
Common lawn sprays such as Weed B-Gone and 2,4-D are not very effective in controlling Clover.* A special Weed B-Gone for chickweed, clover and oxalis is more effective than 2,4-D or regular Weed B-Gone.
TARGETING BROADLEAF WEEDS
CULTURAL CONTROL
You can control dandelions, thistles, buckhorn and broadleaf plantain, chicory, white clover, spotted spurge, pennyworst, field sorrel, ground ivy (creeping charlie), creeping jenny and mouse-eared chickweed by digging. This is most effective in the spring (April or May) when weeds have their lowest food reserves stored in roots. In the fall, food reserves are at their peak and weeds are more likely to grow back after digging. You can reduce food reserves, however, and kill weeds by periodically digging them during the summer. Try to dig or cut the roots as deeply as possible (3-5 inches).
CHEMICAL CONTROL
Herbicides containing 2,4-D, MCPP, or Banvel (dicamba) will control most broadleaf weeds. MCPP is particularly effective on chickweed. Dicamba should only be used on difficult weeds, however, because it can leach through the soil and be absorbed by tree roots, harming or killing the tree. Most lawn and garden plants, especially tomatoes, are very susceptible to herbicides that kill broadleaf weeds. Therefore, apply these chemicals to lawns only when necessary, and do it before or after the gardening season. Most broadleaf herbicides are very volatile (become a gas) at summer temperatures commonly above 80 F and the vapor can drift, injuring nearby sensitive plants. Furthermore, these herbicides are more effective in controlling weeds, especially dandelions, in the fall. In the spring, herbicides tend to accumulate in the dandelion flower rather than in the roots. During fall (late September or early October), chemicals quickly move through the entire plant, and new weeds are less likely to fill in the open areas left by the dead weeds.
I have the same problems you do, so I'll probably be doing the same thing...
Greg