I wish I had known what you know when I was looking at programs for my kids! You have a lot of great options actually. I was disappointed in Headsprout because it taught very few of those basic phonograms. It did do blends (like ip and cl and stuff like that) but I had to teach the vast majority of the phonograms and practice them on my own so I was very disappointed in the money I spent for what I saw as an incomplete program. (Note: incomplete because I wanted my boys to learn all the phonograms). I spent a lot of money and then taught my kids to read on my own and so I regret the purchase even though they did enjoy the lessons. It also didn't teach the first 26 (alphabet letter) sounds. Kids have to come in with that information for Headsprout.
Leapfrog letter factor videos are great at teaching the first/most common sound for the alphabet letters. Example: A is the short sound but they don't do the second and third sounds for a (long a or /aw/). If you don't mind teaching the multiple sounds certain letters make (there aren't very many that make multiple sounds--a, e, i, o, u, y, g, c, s I believe) it's a great start for a young child. That said, they teach the name and sound (A says /a/ (short) A says /a/).
Fun With Phonograms
http://funwithphonograms.com/?page_id=147 materials will teach all the letter sounds with Phonogram Circus and they are working on a DVD for their Phonogram Circus that looks really fun based on the sample they have on the website (it's A so you can see the difference between how they approach all the sounds and Leapfrog just teaching the first/short A sound). It would be my choice for a child over Leapfrog when they get that DVD finished. Their phonogram zoo materials introduce the other phonograms.
Any Spalding or Orton Gillingham type method will do what you want in a multi-sensory way. Sing, Spell, Read Write would do what you want and be fun (not sure of cost for that one) and it's Spalding so will do all of it for you. Sensational Strategies would be a really fun introduction to the method in an Orton Gillingham approach which is generally slower than the Spalding approaches. It won't take you all the way but goes far and does the work for you. Go Phonics would be an expensive (very) but complete and fun option. Recipe for Reading (Orton Gillingham approach) or Writing Road to Reading would be cheap but you'd be doing the work to put together the program based on the book. The Spalding/Writing Road to Reading would be more work/complicated but most complete for what you want of the do it yourself options. The Recipe for Reading would be easy to implement I believe.
I've also got a free source for Orton Gillingham curriculum with complete lesson plans that's really terrific and if you'd like it I can link. I've got enough resources to put together an absolutely wonderful program for free!
Another potential option that is probably easier to teach but also not as multi-sensory might be Explode the Code. I've not seen it but I'm nearly certain it does writing along with the reading. I know it steps them through the phonograms. Bob Books and Nora Gaydos readers to follow up can be used for reading practice along with Explode the Code or Orton Gillingham or similar approaches. I think AbeCDeDarian might do what you want as well though I've not looked into it as much. Dancing Bears is another thing you might look into. There is another too that I'm forgetting right now. I'm not sure of the handwriting component of either of those programs but they are solid phonogram based approaches to reading.