Horses respect those who command respect and follow those who know what they're doing. These things can't be faked (horses are good at reading people) but they can be learned.
To me, gaining a horse's respect begins by getting his attention. If your horse is disregarding you, chances are his attention is somewhere other than on you. I want my horses to be totally focused on me and relaxed at the same time. That's my ideal situation. To achieve that from them, I have to be able to be that way myself. Ray Hunt said that it has to come from inside the person, to the horse, and then you can take it back.
It sounds like your horse is already fairly at-ease with you so you're halfway there. IMO you're right for not wanting to beat your horse with a whip. If you did you'd most likely sacrifice that comfort that he feels when he's around you.
So how do you get a horse's attention? Same way you'd get a person's attention. If you say something to someone and they don't hear you, what do you do? Hit them with a stick? Hopefully not. Talk louder. Get their attention however you can.
Learn to be more assertive with your presence, project your intent through your body language more clearly and emphatically and the horse will respond. The stronger your body language becomes, the less you'll need to rely on whips and such.