One rolling cabinet that both adds and removes moisture. The dehumidifier sits at the bottom and blows left to right. Its water is pumped up into a shared tank, and the humidifier sits on top of that tank with its wick standing in the water. A water line tops the tank up only when it runs low.
Estimated parts total
Rough estimates from typical US retail prices, not quotes. The side-blowing dehumidifier is most of the cost and is what puts this above the $800 target.
Drawings
Fig. 1 · Outside
Counter height, two feet wide
The bottom door opens to the dehumidifier filter and the top door to the humidifier wick. Air enters on the left and leaves on the right, so keep about a foot clear on both sides. The water line and overflow hose come out the back.
Fig. 2 · Inside
Dehumidifier below, humidifier above, one tank between
The dehumidifier's pump lifts its water into the shared tank, and the humidifier's wick stands in that tank. The float valve only adds tap water when the dehumidifier hasn't made enough, and extra water spills over to the drain. The electronics sit in their own bay at the top right, above the water.
Fig. 3 · Water and control
One tank, two ways in, two ways out
Water reaches the tank from the dehumidifier or, when that isn't enough, from the pipe. It leaves through the humidifier's wick or, if the tank fills up, the overflow hose. A UV-C lamp under the lid keeps the stored water from growing bacteria. The shutoff valve stays closed unless the controller holds it open, so a power cut or a wet leak probe stops the tap water.
Fig. 4 · Airflow
Bottom air goes left to right, top air goes up
The controller picks one machine or the other from the bedside reading and rests in the band between, so the two never run at once.
Sizes assume a low-profile dehumidifier that blows side to side (crawl-space style, about 20 × 12 × 13 in) and an evaporative wick humidifier about 14 × 12 × 11 in. The cabinet grows or shrinks with the exact models you pick. Prices are rough estimates, not quotes.