It's funny you say that Kenny, because I'd actually come to a similar conclusion: it's all because my movement sucks.
For example, I can't do the toe-touch (I'm assuming you mean the one from Athletic Body in Balance). Not even close. I've been too scared to try it because I'm scared of flexion, but I guess if Gray Cook recommends it it's probably a good idea. I was just waiting til I could bend pain free before trying it.
So what's the step between doing it on the floor and on doing it on your feet?
Don't be scared of flexion. Flexion is necessary. Also, there's a difference between how you should be able to MOVE and you how should TRAIN. Just because it's preferential to avoid training lumbar flexion in the gym, does not mean we should avoid having the ability to flex the lumbar spine.
You can't achieve real stability without first having full mobility. You need movement first. This works from the perspective of viewing your body as an integrated unit (specifically - the joint by joint approach). For example, if your hips and upper spine are restricted, then you lose stability at the lumbar spine via compensation. In that case, plank and bridge all you like - you're always going to rely on lumbar spine too much if you don't free up the movement you SHOULD have in T-spine and hips. In fact you most likely already have a stable lumbar spine but you won't realise this until you free up movement else where and give it a chance to realise it's potential (for stability and the transfer of force). YOu may not even be doing a movement that requires full ROM at T-spine and hips but, your body doesn't know any better (because it doesn't know what full T-spine and hip mobility feels like), so it will rely on lumbar spine anyway.
It also works from an isolated perspective, too. If your lumbar spine can't flex, then you're stuck in extension. How is your body able to get into the middle, or midline (remember, to go from extension to neutral, you need to flex) - the position needed to utilise the surrounding local and global stablisers. Your abs, glutes, even multifidus, transverse abdominis, for example, are at a mechanical disadvantage if your lower spine is stuck in extension and can't flex and get into the middle. Now you need to rely too much on the lumbar extensors, hip flexors, QL,etc, to get stable. Charlie Weingroff refers to this as the "core pendulum theory". Opening yourself up to true stability won't just keep you out of pain, it'll make you lift better/more!
The next step from floor to feet is too specific to try and guess over the net. I'm hoping your physio is going to nail this for you. The example i used previously was squatting. If I get someone - particularly female - who can't squat well or deep, I lay them on their back, get their spine into neutral (normally by getting them to put one arm under the lower back), and lift the knees. Normally (especially women), they will be in a perfect deep squat position only, they're lying on their back (I clear the ankles via other means). Now, sometimes, they genuinely need to do all the stuff you've been doing and, "bam", couple of weeks later, we have a good squat. Other times, I just need to coach them how to squat properly and they achieve it within 20 minutes. I guess my point is I need to see you move to help with that.
Worth saying that failing the toe touch doesn't automatically mean you need more lumbar flexion. A lot of the time it's hips that lock up on this test. The toe touch, I bet, will be one of the first things you are asked to do.