I'm with Tom on this, if water is a problem why add more? compost tea is derived from compost so there honestly is no difference except you are a little less vulnerable to mildews, and fungus when top dressing with the compost vs using the tea. That said compost tea is a great thing to use in the garden but wait until it needs watering.
If overcast, rain and cool weather is a common problem in your area you may want to invest in some red plastic mulch. This will help reflect what sun you do get back on the plant and the red spectrum in light promotes flowering. I wouldn't suggest using plastic mulch on a mass scale but for 1 or 2 rows of tomatoes it should work great for you.
