Seems like there are a few operating principles here. As long as you try to honor all of them, you're on the right track. By all means, take the time you need. You shouldn't feel guilty waiting until April 15. That's the time allotted to you. All of us on waitlists just have to live with that. The balancing principle, though, is to try to keep only one offer at a time. Each time you get an offer, re-evaluate and let one of them go. It's only fair to the waitlisters and to the departments trying to match people up with their funding. Now the complexity comes in when you get a "half-offer". You are admitted, but are waiting on funding. Or you have funding, but only partial, etc. In those situations just do the best you can. As for the visits and incorporating them into your multiple offers, well, I think the principle should be (but isn't necessarily) that the in-person visit is really just a tie-breaker. You've already done enough research to know you'd be WILLING to go there and that it would be a good fit. If you're struggling between two essentially similar offers, then the in-person visit is the tie breaker.
Well, that's my decision matrix anyway.