OP I feel a little badly you're being jumped on, me included, so just want to stress that everyone has the horses best interests here and we are really trying to get across how serious this can be. The horse is in pain and is not diagnosed and you are guessing at what to do, lots of which may be making it worse.
I'm sure you don't want your horse to be suffering and I get diagnostics (x-rays, ultrasound, etc) can be expensive but some situations call for all in, a) so your horse is happy instead of in constant pain (for months) and b) so the issue can be fixed, hopefully fully and you can go back to enjoying your horse instead of wasting money on things that won't work and very well may be hurting, you are spending more money and time on things that are a waste at this point instead of just fixing the problem.
Have you even asked your vet for advice on what to do short of diagnostics? I would be VERY surprised if your vet said "go lunge him!". Many horses MUST be on stall rest, usually long term. This stuff is really serious. A little frolic (or lunging) can undo any healing and make it worse.
Pointing the toe while at rest is just him showing how extremely he hurts, that he doesn't want to put ANY weight on it even when he's not moving. (Fwiw I haven't seen a navicular horse do this though don't have a ton of experience)
So please, don't think we are "out to get you", we really are trying to help, both you and the horse.
It's just a shock to me, and I'm sure to others, when we read and say "ok, ok" then "WHAT??!!" when you just guess. I'm sure you can understand why it's not making sense to me that you may not want to turn him out and keep him on stall rest (the right thing to do, a stall sized paddock outside is suitable for an unhappy horse if it makes him happy and quiet, just don't let him move, it doesn't need to be "inside" unless you're walking a distance to it) then you just lunge him? You need to run stuff by the vet, he doesn't need strength he needs healing. Have you ever pulled a muscle? How would you feel if someone made you move it over and over and over to "strengthen" it.
So please just take a step back, don't let us scare you off, and just try to listen to what we are saying. It will save you a lot of anxiety too to just know what you're dealing with!