I'm likely not going to be as helpful here as I'd hoped to be with usable info on the Lower Canyons of the Rio Grande. Looking through gauges and stages, etc., across a few years doesn't suggest a season as truly reliable to me. duNord also indicated essentially the same in his note above. There's a "monsoon season" of late summer and on into fall rains that bring the river up, but for some of those you might have to be sitting on the riverbank ready to catch them. It's likely not that bad, but I guess some runnable periods can be pretty short-lived.
I didn't really get anywhere with research, but here's some info on the run.
My wife and I launched Feb 27, 2019 on the Rio Grande at Heath Canyon Ranch, site of the closed and uncrossable Gerstacker Bridge between the USA and Mexico. This is a private ranch collecting a trespass fee for access. The Rio Grande Village gauge, which is about 33 miles upstream of here, was 150 cfs or between 2.62 and 2.63 feet on the height gauge and dropping very slowly. A day later it was 145 cfs, so not fluctuating a real bunch. In contrast, this year, same date -- Feb 27, 2024 (about 8 months ago now) -- the flow was about 40 cfs with a gauge height of 2.15 feet. I'm not looking up Dryden gauge levels. Interested parties can do so themselves, not that it would be meaningful. Not sure that 40 cfs is runnable, but the Aulbach guidebook I have says the lower limit for canoes is 1.7 feet on the Rio Grande Village gauge upstream. Has the gauge been "reset" at a different reading between then and now? I have no clue. Likely not but a local outfitter may know, and some of them might disagree with Aulbach on runnable levels. The disparity in perceivable flows at Heath Canyon may just not be evident or show reliably on the gauge upstream. And how long does it take the water to flow the 33 miles from Rio Grande Village down to Heath Canyon? That's not really a factor.
As I mentioned before there are a lot of (small) springs that come in below the Rio Grande gauge which likely keep the downstream flows more stable. For the heck of it, the Dryden gauge at the takeout was recording about 510 cfs that day with a gauge height of 5.17 feet (Dryden gauge records in metric and I'm converting). The two gauges can't correlate too closely. The two gauges are 116 miles apart, and how long does it take the water to flow between them? Where I live and usually paddle I'm used to figuring an average current speed as about 4 mph. That means the water travels about 100 miles a day. At really low flows like this, I'm sure it's slower than that. Maybe a day to get the 33 miles from Rio Grande Village down to our launch at Heath Canyon (aka La Linda)? It sounds like a lot of what we run on here is springwater discharge, and what is coming from upstream makes it enough to be floatable for canoes. More likely at low flows it's more like half and half or more? The springs betweeen the guages seem to contribute on the order of 300-350 cfs. I don't know if there's any fluctuation during the year.
Aulbach seems to provide some conflicting info as to runnable levels, but maybe I'm just not reading things right. He says a minimum of 100 cfs on the Rio Grande Village gauge, which means our run launching at 140-150 cfs is close to bare minimum, and I'd agree with that if I'm allowed to use my one data point curve. He also says that 1.7 feet on the gauge is minimum. That 40 cfs of this year would be too low of discharge, but the gauge height was listed as over 2 feet, which to me is "way over" minimum. Has the gauge been reset? I'm sure an outfitter would be able to clear things up, but I'm not likely going to be running the river again, so it's your trip, you do the needed research and judge things for your skill levels and those you'll be with. I'm sounding like a government bulletin here. Maybe I'm making this more complicated than is needed? With the 2024 election that just finished, get your run in before the wall goes up or the river is closed to lengthwise travel, much less across it.
Anyway, we took out on March 8, 2019, and the Dryden gauge, which we passed getting to the boat ramp indicates a flow of about 490 cfs, stage height on the gauge of 5.1 feet, again converting from metric. That is slightly less than the readings on the day we launched. The Rio Grande Village gauge upstream on that day was maybe 146 cfs with a gauge height of 2.62 feet. Not significantly different on March 8 of this year (2024) the stage was 2.16 feet and between 37 and 38 cfs discharge. Not that that has any bearing on our trip, but again may help correlate put-in and take-out gauges for you. Also not looking up Dryden values for this year.
Like duNord, we did our Lower Canyons run in 2019, though we were on it in Feb/Mar and he was in Dec the same year. My wife and I wanted to do Santa Elena and a couple of the other canyons mentioned by duNord, so I was in contact with Mike at Desert Sports summer of 2022, who kept indicating to me that there weren't any signs of the river likely coming up and allowing a run of those sections. He had said when I'd quizzed him earlier earlier that November is a more reliable month for decent flows in the Santa Elena section, citing the reservoirs releasing water to the Rio Conchos as being needed, and they were all low. We scrapped our trip, but I checked later and the river did come up, which allowed duNord to go on his, and I wish we'd have done it too, but it was likely a good thing we didn't as I'd already started having my vertigo problems. I haven't done any checking since, though it sounds like duNord has.
Does any of the above make sense? It's certainly not very helpful.