The OP was specifically asking about a 20 bore quail gun. Not specifically a SxS, but he'd like to get more into them. I understand your thinking, but there
could be other problems in play.
On many hunts if you show up with a 12 bore for quail, you will be given "a look" for not having the "appropriate" upland gun for the quarry being hunted. And on some of those hunts they actually require a sub-bore shotgun, not allowing anything larger than a 20. In truth, some places really want you shooting a 28 bore to be a proper sporting gentleman.
@Travis2282 - After talking to the owner of CSMS at the SCI show and seeing the extensive collection of 20 bore (used and still in excellent condition) shotguns, I'd not hesitate to give him a visit. I'd be surprised if you didn't place one on order AND walk out with a used one as well.
I've met these pompous rednecks. They are shooting 1-1/8 ounce 20 bore loads in guns that weigh 7.5lbs and taking issue with an English 2.5" or 2" best gun shooting a 3/4 ounce load. That's only because they are ignorant and because they don't understand what they are looking at. I've rarely seen a rigid rule on this topic, only a guideline by the ill informed. Once I inform them, they usually sheepishly admit their gun is packing more wallop than mine, weighs more, and if anyone is "cheating" it is them since they are using a shell that is way over the power that created "the spirit of the rule".
But anyway, you definitely can get a nice 20 bore. About the nicest/cheapest 20 bore I can think of is a beretta manufactured Orvis Uplander 20 gauge O/U with an english grip stock. Those go for $3000-$4000 used and they are about the only 20 gauge O/U that doesn't weigh too much. Next gun in their weight class as an O/U 20 bore is going to be in that $30,000 range or more, used, of a modern British design ala Woodward styled.
If we're talking side by sides, you can absolutely get a spritely used boxlock non-ejector Birmingham gun in 20 gauge (or smaller) that is lovely, but you just can't get that gun used for $3000 and right now English 2.5" 20 bore shells are hard to come across compared to 12 bore.
I like high grade quality guns and best guns. With frugality, anyone on this forum can have the luxury experience, but you have to make tradeoffs. 96% of all English shotguns (where the quality-price ratio is optimal) were 12 bore guns. The remaining 4% were all the others, of which 10 bore was easily 1%, 16 bore were 1%, and 20 bore were 1%. Every other gauge from 2-4-8-14-24-28-32-.410-9mm make up that last 1%. (many of you may be unaware half those gauges even exist)
So for quail, for the money, for the weight, and to own something that would be $50,000 to have made new today, I'd suggest a between-the-wars E.J. Churchill XXV ejector 12-bore that weighs 5-3/4 pounds and has 2.5" chambers. Cost is $3000ish. To change only to a 20 bore for the same gun, you're paying $6000-$8000. To make it a 28 bore, you're paying $12,000-$18,000.
Whenever I show people a variety of shotguns we have at the house, they never ooh and ah over the $14,000 MSRP Spanish piece of crap, nor the Orvis Berettas, nor any of the other items in the roster, they always ooh and ahh over relatively low cost British Boxlock Ejectors. The quality is that high, the resale versus MSRP is that low, and they weigh nothing.
OP, if you want a true quail gun and you're flexible on your budget, I have a circa 1950 baby frame, near new, O/U 28 bore ejector that weighs 5.5lbs and has its case and accessories. But that's a $6500 gun wholesale, the least I'd take for it. (Only selling because its nearly 2" too short for my giant stature.)
Gauge gets smaller, price doubles each gauge step.