The typing of this CAP is not the first thing I would discuss as there are actually quite some types that can at least check lots of threats that are mentioned. For some Pokemon it is just enough to get a non-super effective hit to switch in.
A lot of power comes from the fact that standard counters share weaknesses which can be typing but also biased defenses and especially low speed, which allows the offensive player to counter in time. Counters are often too predictable in this metagame.
We should decide whether the CAP should be able to come in repeatedly or have a higher chance to stay in, after the threat it is meant to counter switches out. The more we expect this CAP to do at once, the higher the BST will be. But this will not allow more variety and the only shift to be expected are the chosen coverage options of our current sweeper.
A very necessary early restriction should be made by getting a vague description of stat limits to not make the mistake to create a Pokemon that simply recentralizes the metagame.
If we make an slightly imperfect raw stat spread and therefore define the expected role, we could alter the needed typing and movepool to fit the CAP´s intention.
It could also help to look at existing Pokemon and discuss what they lack to counter certain threats. Weezing for example might be a better Dragon and Fighting counter, if it could hit back harder and recover reliably. But he has the right mixture of typing, ability and defensive stats to be viable, although he does not hit the 500 while being a levitating steel/ghost type. I guess Ludicolo would be an even better research object to get some information.