Without really answering your question right away, I will make the comment that it is wise to find out what is wrong before launching into various back remedies. If there is pain or any other sensation in either leg, foot inc. toes...coinciding with your post walk symptoms...treat this seriously.
It may be that you would be greatly improved by a good chiropractor, but unless you know what is wrong, the manipulations may only serve to exacerbate the problem.
If you can get an MRI scan do so, but your GP may not want to burden the health service until you are in greater need...that's a shame, because early awareness of a problem is a great benefit to maintaining a normal life. The problem for spinal surgeons is that even with a good MRI, unless there is a very clear fault, things like bulging discs - worsening after long walks - are so common, (and often cause no symptoms whatsoever), that they almost certainly will not want to draw any firm conclusions from this alone; leaving you no further forward.
It sounds as though you are going down the right route. Back and tummy tone is vital, and a middle of the road approach is at least safe. It is my unqualified opinion, that prior to exercises that will cause a reduction in the space between the rear edges of the lumbar-vertebra .( "The Cobra" in Yoga), it is wise to stretch the lower back by some means. This varies in relation to your overall fitness, but can range from an inversion table, to hanging through a loop from a handy branch, through to the use of improvised or real crutches.
The attachment of the discs to the vertebra is very strong, but the periphery of the disc is not exactly bullet proof. If you can make any reduction in the bulge before crunching it, you are going to be way ahead of someone launching into the exercise without much planning.
Good luck