I don't really think barrel length/contour has any affect on accuracy in a cold barrel, I've got 16" barrels that are just as accurate as my 26" barrels, now length and contour do have great effect on velocity and heat disapation, which will affect bullet drop as distances increase and accuracy as barrel heats, a heavy barrel will take longer to heat, but it will also take longer to cool, but if your strictly varmint shooting, you won't be firing that many rounds in a row for the barrel to get hot enough to greatly effect accuracy, if you do get it hot, leave the bolt open and switch to your spare rifle,
a heavy barrel also adds weight to the rifle which helps you hold it more steady,
a 20" in 223 should work just fine out to 300 yards, I don't think any but the 40 to 52gr. varmit bullets can be driven fast enough with the 223 to reliably blow apart much past 300 yards anyway, they will expand a little, but you won't see the explosive expansion like they do at shorter ranges, which might allow a gut shot animal to crawl into a hole and die, instead of blowing the hell outta him and killing him instantly,
last time we went PD hunting, I used a hornet loaded w/45gr Bee bullet out to 125yards, a 223 w/50gr vmax out to 250 yards and a 22-250 w/ 50gr vmax for 250 yards plus.