You’re so golden
For starters, Mandibuzz, Clefable, and Toxapex can at very least check both sets with their most common variants barring Shadow Ball drops or crits. But beyond this, any argument about Dragapult being a problem should not stem from this at all.Can you tell us what 3-4 items and 3-5 sets you're talking about? I could be wrong but I don't think there's any one pokemon OU (or even good mons below UU) that can deal with both the specs and dragon dance pult sets.
It is incredibly easy to decipher if Dragapult is DD or not from team preview. DD is super uncommon to begin with and only has any viability on more offensive teams, particularly on hyper offense. And on hyper offense, you seldom see specs Dragapult as locking into the wrong move (or even the right one after a fodder) can lead to a huge problem as a free turn is suddenly opened up for the opponent, which HO struggles to deal with.
If you struggle to decipher Dragapult sets at preview (beyond boots status vs specs, which have a massive amount of overlap and you can even figure out some of the time) when talking about DD vs specially based, that’s absolutely on you as a player. If you struggle against DD Dragapult in general, a set that has been subpar and uncommon for months, then that’s far more on teambuilding issues than it is anything else. There are a myriad of viable checks and counters.
Choice Specs Dragapult is a menace and I understand frustrations about it, but the versatility card is being misapplied here and other sets simply do not belong in the same discussion.