The research actually shows that "joined manuscript" is both faster and more legible than cursive, especially at maximum speed. It doesn't degenerate into a scrawl or scribble the way the "loopy" styles do.
Kate Gladstone is the handwriting go-to guru, her website Handwriting Repair has a ton of resources on the topic. She recommends a number of the italic and quasi-italic styles, which have always been dominant in the UK and Australia.
It's untrue that traditional cursive will eliminate, or prevent, b-d reversals and other such anomalies. I've had a number of students who consistently made b-d errors in cursive -- "The bog is darking," and so on -- even though the letters did not look anything alike. Kids with graphomotor output issues have a terrible time learning traditional cursive writing, and their writing always looks like chicken tracks despite their best efforts. Italic and manuscript-style joined cursive, a la "Handwriting WIthout Tears" yield better results.