gee... no one wants to jump in here? lol!
Take this all with a grain of salt. I've learned more in this past year than I have in the past 30 years of riding, so my opinions and ideas are subject to change! Obviously without seeing your or your horse, we can only speak in the most general of terms.... but I'll take a crack at it.
When a horse is having trouble with something like this, I go back to very basics--VERY, like the voice aid. It's the most unobtrusive aid that does the least 'interfereing'. So I'd start on the lunge and really establish the 'terrr-ot' cue. Lots of transitions on the lunge. I tend to forget to use my voice under saddle--since it's not allowed in the show ring--and it sounds like you're already doing the lunge work, so just add the voice if you're not. Another really useful 'aural' cue we use is the 'calm down' cue. We use a certain whistle, going down in pitch, and the horse tunes into it. It can be a come down or calm down from anything... but it's helpful too if we're rushing around like a giraffe on crack.
Then use the voice while riding. Voice only/first if it works--and you trying to stay as stable and balanced and 'out-of-the-way' as possible.
As far as ME, canter is very easy to get your hips sort of locked into the rhythm... and truly, usually *all* it takes to canter down to trot is to break that, and let the inside hip drop back OUT of the rhythm. I'm not going to explain this well

Your inside hip is a bit forward to canter... your entire pelvis swings once at each stride... to canter-to-trot I walk the inside hip back and outside forward--in the way that they would work in the trot. The horse follows.
Have you ever been on a horse that will collect the canter all day but won't down transition? This is the ONLY way to get that horse to trot... you've got to put your seat into trot, and the horse follows.
Make sure you're asking for the transitions on an uphill, not a downhill. And all but the flattest of indoors have little uphills and downhills, even if they're not dramatic.
Make sure the canter is foward enough before the down transition--if the canter has fallen on the forehand, the trot can only be the same. Sometimes I marvel at the folks who canter around and around trying to 'improve' it, when it's only transitions and gymnastics that improve a gait--not just going around the same as you were...
Try doing the transition in the middle of the short side... think shoulder-fore in the first corner, transition, then sholder-fore through the second corner, using the bend to get the 'speed' to translate to impulsion. Try to keep the inside hind... Changing after a diagonal--just before you come to the wall to take the new direction can also help the horse to rebalance.
And the last sounds a bit counter-intuitive, but works for some horses... do canter-walk instead of trot. Then just tons and tons of transitions--walk-trot-walk-canter-walk-trot-walk-canter-walk... lather, rinse, repeat. You'll build the strength and coordination needed and one day you'll ask for a walk and instead get this lovely trot and there you are.