I cut small pieces all the time on a coffee table. Technically, on a mat that's on the table - but I think most everyone assumed that!
I've also used a flat TV tray for a cutting table. That worked out well, too - for small pieces.
Maybe cut the long strips standing up - and then cut the long strips into the smaller segments sitting down?
PS Because our couches are kind of low - I sit on a pillow so it's easier to get up.
PPS I think it's important to get up and down fairly often -