taxi is still your cheapest and most convenient...unpleasant experiences with taxi drivers rather a exception as taxi are registered and the hotel name and/or destination verified by staff
if not there are plenty of booths with limo services at the airport...but of course more expensive...or let the hotel organize one

another option could be - as the hotel is not so far from Ratchaprarop station - to take the airport train until there and walk the 700 meters to the hotel or take a taxi from the station.

it depends a bit of what ariline you fly and whether cattle or higher (with fast track), but as your hotel is close to an entrance to a highway, it should even during rush hour not take more than 1 hour to get to the airport...so 0630 or 0700 should be fine