By and large, Double Quotes is won not with big words, but with small ones. 2 letter words particularly, will help you keep your move-average high and improve your chances of forming a quote word. Memorising the following list is probably the single best thing you could do to improve your score.
AA AB AD AE AG AH AI AL AM AN AR AS AT AW AX AY BA BE BI BO BY CH DA DE DI DO EA ED EE EF EH EL EM EN ER ES ET EX FA FE FY GI GO GU HA HE HI HM HO ID IF IN IO IS IT JA JO KA KI KO KY LA LI LO MA ME MI MM MO MU MY NA NE NO NU NY OB OD OE OF OH OI OM ON OO OP OR OS OU OW OX OY PA PE PI PO QI RE SH SI SO ST TA TE TI TO UG UH UM UN UP UR US UT WE WO XI XU YA YE YO YU ZA ZO