BB, what gait does your horse do on his own naturally? Like a running walk or foxtrot or something similar? He clearly is more diagonal than lateral for a gaited horse since he so easily goes into a trot on the lunge. Having gaited horses myself who have difficulties with their canter (legs go all different directions like an octopus, sometimes the back legs are doing something different than the front) I've found that most of it is just learning to work those gaited muscles the right way.
The first thing I did with one of mine who did that was get the first transition down good - that first transition was going from a fast dogwalk to a decent speed into their intermediate gait. They need to be able to do it going straight and on turns and stop/go on circles without tripping or fumbling or getting their legs tangled up - the transition needs to be flawless and smooth.
THen I started work from the intermediate gait to the canter - but not on the lunge. I started teaching the canter first in a STRAIGHT line. Find a nice long easement/grassy area or pasture and go into their most comfy (for them) intermediate gait (whatever it might be) then ask for the canter. Once they do pick it up (the first few times will be the wild octopus) then try and hold it for just a few strides, then slow to the intermediate gait. Repeat a few times, only on a straight away - don't try to canter on a turn for a long time until they get the transition down. If you have a nice big log to put in your path or a pole or something about 12" high, sometimes as they hop over it, they will canter when landing on the other side and that too, is a great way to help them get the feel.
It looks as if this horse is being rushed into the 5th grade when he is still learning his ABC's in the first grade. How is his/her slower transitions in slower speeds? What gaits does this horse have? Most gaited horses that are more diagonal like this guy have a few different gaits to offer. Can you isolate each one at different speeds with a smooth flawless transition? This horse needs more work at slower speeds it seems - even tho he is trying his heart out for you, it doesn't seem he quite knows what to do with his feet. You will have to be careful since working him on the lunge over several weeks like this without any improvement is only telling him that you are satisfied with this type of movement.
I think you need to take him off the lunge, get on and have someone take some video of you riding at the walk, a fast walk, his intermediate gait (or gaits) and then show us what happens when you ask for the canter. Meanwhile, try working on straight paths and don't try to work on circles or turns just yet until he figures out his feet.
He needs to be able to handle himself at the slower speeds and have flawless transitions within his intermediate gaits first before the canter comes into play and I'd love to see some video to see if this is the case. It might just mean he needs a little backing up and revisiting with the basics. It will take time, and that is okay! Gaited horses are wired differently - they don't all come from the same mold.