Salmonsweet,
Brushes for fabric are not real stiff, there is a brush just for fabric painting. Check local craft or art store, I will be glad to send brushes to you. I use regular acrylic paint adding fabric medium. About half and half of paint and medium.
Tape does hold fabric in place. I like cardboard as a backing support when painting. Cardboard can be a box, they are strong and don't bend easily.
Hope this helps. Please let me know how I can help.
Have a blessed day.