I'm sorry, but from what I know of bettas, some of the regular rules of fishkeeping don't apply here!!!
Bettas... natural in-the-wild bettas... live in steaming rice paddies and marshy bogwaters that are soft, acidic and often full of decaying vegetation. Part of the reason bettas and other labrynth fishes adapted to breathing surface air was because the natural water conditions were so harsh on normal fish's gills and was generally stagnant and had little to no oxygen content. They also deal with heavy rains, flooding, and monsoons which cause the water conditions and depths to fluctuate during different times of the year.
They are also used to cramped living conditions due to the low water levels forcing bettas into encounters and struggles for territory in shrinking tropical pools. And when the betta was being domesticated for the generations, it was natural to keep them in nothing more than a jar or other small container until it was to be taken to a fish fight or bred for more bettas.
Granted, today's betta is a much softer, frillier fish than it's tough-as-nails wild counterpart, but a lot of that same sturdiness and adaptability has remained in the species. It can handle rough water conditions, no filtration, and cramped living spaces because this is how this fish has lived and been kept and domesticated over the generations.
I get so tired of people treating the betta like it's as long-suffered as the goldfish. Yes, keeping a goldfish in a bowl is inhumane and terrible treatment... but not all fish are created equal. The only thing inhumane about the 'betta bowl' is the lack of controlled temperature (since bettas like it at least 74 degrees F or warmer!) and the myth that Bettas with those Calla lily plants don't need to be fed. Now THAT is a crock of crap! Bettas are carnivorous and only eat vegetation when they are STARVING.
So there. That's the truth about the betta. My opinion? Go ahead and add him into the new tank and let him adjust on his own terms. He may not be as hardy as his wild counterparts, but I've never seen a betta go into shock and die from a change in water. He might discolor for a brief time, but that's going to happen with any fish delivered into a new environment.
I respect a lot of opinions here and many of them go off of years of practical fish keeping and enjoyment of this hobby. But you can own a fish for its entire lifespan and never know the real nitty-gritty about it's preferences, tolerances, and origins. Most people think they can have a betta in a tank for a few years and know everything about how it should be treated. But not all 'fad fish' are created equal. Yes, goldfish in bowls swim in their own waste which eats at their already starved gills until they slowly suffocate to death in a bliving space that would be like stuffing a 6'6" man in a broom closet and asking him to thrive. But that's goldfish, people... not bettas.
Granted, it's not bad treatment to keep them in large, filtered tanks... but some of the 'insisted requirements' around here are honestly over-the-top in my opinion and to insist them on anyone interested in keeping a betta is so unecessary, especially given the information above-mentioned.
I sincerely apologize for ranting in your thread, Caresteph, but this gets under my skin like nothing else around here on these Forums... G__G