The first thing I think of when the child is demonstrating difficulty with drool management and slushy speech is tongue thrust.  It seems that the child may have difficulty using his/her tongue as a separate entity from the rest of the mouth (using it independently).

Tongue Thrust should be treated by a therapist who has experience and additional training in that area.

However, if you have no other options:

• Try the tongue exercises from this webinar: https://members.slpsolution.com/foundational-oral-movements-for-treating-the-r-sound-webinar-recording/
• Try working on the drooling: https://members.slpsolution.com/dealing-with-drooling/
• Work on the lateral lisp: https://members.slpsolution.com/lateral-lisps/