I suffer lower back pain myself, ranging from always there to shit I can't move when it decides to seize up completely.
I know mine comes from a gym injury and bad posture/core strength etc.
Being a cyclist of many years I am strong posterior and weak anterior muscularly, in as much as my pelvis tilts forward when standing.
Standing too long will make my back ache (and spasm if too long) unless I think about tensing my lower abs and glutes to pull my hips level.
Re recumbents, I have ridden them for years with no issues with my back pain. I have upright bikes also and spent most of last year riding fixed gear all over the place including camping.
Speed on a recumbent comes with practice of course, Balance and riding one the same.
I have a range of recumbents (Ice S trike, Bacchetta Giro, M5 CHR) and have ridden audax on all of them.
Trikes will be slower than most 2 wheelers and harder uphill obviously due to the extra weight.
Bacchetta do a range but the lighter ones are faster. My Giro with 700 wheels I tend to get around a 200 in about 8hrs moving.
The CHR is a very quick bike and the ones I have done recently have been fast!
(200 in 6.40 moving, 300 in 10.40 moving, 400 in 13.40 moving)
It can be a long learning curve changing to recumbents and building the distances up (different muscles etc) but some will pick it up quickly.
A trike can be ridden by anyone as you will only fall off of it if you go mad
The Bacchetta with the adjustable seat is a good starting bike as the seat can be laid back as you get used to the balance.
The CHR took me a while to feel comfortable riding it even though I've been riding recumbents for about 14yrs.