There are two main methods I use to attach the drawer fronts accurately no matter how bad the action of the drawer slides are. If are no fixed dividers between the drawers and you can remove the drawers, I do the following. Remove all the drawers except the bottom one. When it is in the closed position, place the drawer front against it and shim the gaps on the sides and bottom correctly. Clamp it in place, slide the drawer out enough to put screws in from the inside. Remove clamps, slide in next drawer up, put face on, shim it up from the drawer below and sides, clamp, slide out, screw in place, repeat until you get to the top. The top drawer is trickier since you can't get clamps on it until after the drawer is slid out so I either put the drawer front on using double stick tape (still shimming it for proper spacing) so that it will be held in place until I get the screw in. But there is another option.
The second method I use which is good for all types of drawers that have handles, regardless if the drawers can be removed or you have room to clamp the drawer front on until you get the screws. For this method, you place the drawer front on the drawer body when it is slid into place. Predrill your hardware holes for the handle before placing on the drawer body. Put a small amount of wood glue on the back side of the drawer front, set in place, shim the gaps just like the other method and add a couple screws from the front into the predrilled hardware holes to hold things in place until the glue dries. Remove the screws, finish drilling the holes and add hardware. You can also add a couple more screws from the inside of the drawer to add more strength. You don't need any clamps and you don't have to remove the drawer bodies but it does take some extra time waiting for the glue to dry.