This is kind of tough to do. You can buy thinners for acrylics that will help smooth them down. Acrylics are always difficult to gradient shade because they’re kind of pasty, they don’t have the smoothness that oil lends to oil paints. One thing that might help is a very soft-bristled brush, like a sable. This will help so that you don’t see the bristle lines. Although if you use sable with acrylic, be sure to clean it very thoroughly after - once paint dries in that kind of bristle you’ll never get it out.
Ha! Dali is one of my favorite artists, but I think the only thing he’s quoted on that I agree 100% with is, “The only difference between myself and a madman is that I am not mad.” 
Thank you for the suggestion above on using a sable brush with acrylics. The pastiness you mention has been the problem and maybe that would help. I’ve been trying to steer clear of oils because I have athsma and I’m unsure as to whether the thinners and so forth would be harmful, but it’s beginning to look like I’m going to have to start working with oils in order to get the effects I want.
Your Dali quote above reminds me of another one along the same line that Dali made regarding the surrealists of the time: “The only difference between me and the surrealists is that I am a surrealist.” He’s one of my favorites, too.
Thanks again for your advice.
No problem I have athsma too, I find that if I use turpentine thinners for too long I feel kind of nauseous, even with good ventilation. I prefer the Eco-House citrus thinner. Pleasant orangey smell and not as toxic. Eco-House is in New Brunswick; you can visit their site at http://www.eco-house.com. I’m pretty sure you can order online from them if you’re interested in anything they have.
Winsor & Newton does manufacture water-soluble oils, FYI. I’ve only used them once and I liked them. You can add water to thin them down. They are still a messy cleanup process, but not as messy AND less stinky than traditional oils. But yeah, I know what you mean. Oils give the kind of depth to paintings that acrylics just can’t.
Thanks for the suggestion. I’ll definitely look into the citrus thinner. It’s nice of you to offer your expertise like this.