Ask them if they've considered Lumbar Spinal Stenosis, which is a condition where there is overgrowth of the bone around the lumbar vertebrae, which causes pinching of the nerves as they leave the spine.
It can cause pain in the lower back, centrally/frontally in the crotch area, and running through either or both hips into either or both legs. It can be accompanied by tingling - a bit like itchy sunburn - or numbness in the lower leg. The pain can be extreme, burning, and not susceptible to normal analgesics - I'm on a low dose of opioid, which seems to control it well enough.
I've had this, gradually getting worse, for 25 years and was only diagnosed this summer after a hideous flare-up.
My basic symptoms are different to yours, in that standing causes my lower back muscles to cramp up and I have to touch my toes to stretch everything out again. I can't walk far because the nerve pressure affects the way my legs work. Actions like pushing a supermarket trolley give some relief because I lean slightly forward to push, which takes the pressure off. Equally sitting - leaning forward at my desk is more comfortable than sitting upright.
The flare-up went through my right hip (red-hot skewer), causing the main front muscle on my thigh to go into permanent cramp, and caused tingling and then numbness across my right shin. The only chair I could sit on comfortably was a bentwood, chapel-type chair, and I wasn't clear of pain even in bed. Sometimes I could only walk bent over at right angles.
There are lots of different nerves leaving the lumbar spine for the pelvic area/legs, so you might have the same condition but a different nerve is affected.
I was referred to a physiotherapist who gave me some strengthening exercises for my stomach and pelvic area muscles - this helped. I was then referred to the Spinal Rehabilitation Unit at our local hospital where I saw the Senior Physio - he listened to my description of how the thing had developed, plus present sympoms, and diagnosed me instantly with lumbar spinal stenosis, and possibly a bulging disc.
It seems the condition may be a lot more common than is presently admitted, because it is difficult to diagnose, and it's almost outside of a GP's experience, it's more a Physio thing. I ws lucky in that my GP did eventually suspect it, and referred me. Now I'm waiting for the results of an MRI scan to see if mine is operable.
Google it - there's lots of good info about it - discuss the possibility with your GP, and ask to be referred to a physio in any case. They may be able to help, even if it isn't LSS.
Good luck!
Viv 8)