First of all, Solid Rock drops your Super Effective damage by 1/4. So a Pokemon will still take normal damage from non-Super Effective moves, and therefore as awesome as the ability is in theory, on paper we're pretty much restricted, due to its name and other things, to using it on Rock and Ground Pkmn, so it has key limitations which people easily exploit. Such as Water/ Grass weakness. So we can throw that ability out the window for starters.
Secondly, do we really want CAP 10 to go into Dragon/ Steel, another type combination with a single weakness, Ground, and then further reinforce it with Levitate? I'm not saying that it isn't a good idea, but if that happens, we should lower the aggressive stats to more respectable levels, such as 50 - 70, for example. After all, it would then have immunity to two types, resist 10 types for 1/2 damage and resist another type for 1/4 damage. That's 13/17 types resisted or suffering immunity. Which would leave four types to hit it back. Quite a large range to take moves hitting it, so in response, we would need to mitigate it's stats somewhat.
Tinted Lens is so-so. On the one hand, we maximize the coverage, but on the other, we allow it more chance of countering things it wasn't designed to. Plus, we aren't trying to make yet another wall-breaker or sweeper, so being able to never do anything less than normal damage would potentially be broken. Especially when we consider Bullet Punch - it would do at least normal damage, and it can hit everything with impunity. So if we chose Tinted Lens, then all priority-escaping moves would end up being blocked, on the simple basis that they'd be using a STAB which moves first and hits everything.
As a response to Huge Power... if we did end up going down that route, we'd possibly create a hugely powerful sweeper. But we could do the same thing, but with Def. or SpDef. instead. That would mean you'd be able to raise it's stats to take special or physical attacks, but the only stat maxed out Base-Stat wise would be HP. It's not a brilliant idea, but it's got potential.
About abilities which change your typing on entry: first of all, that ensures our Pokemon is a Normal type. However: If I send out CAP 10 against Charizard, it can change into Rock, Water, Electric, Rock/Water, Rock/Electric, and Water/Electric, if we just look into counter-attack stats. Those six options are without considering the getting hurt options. How would the Pokemon choose which of those it would become? It's much too difficult an ability to get the AI to choose for you, so that means we need to let the player do so. Which quickly makes the Pokemon broken, as the ability is average, so the stats would improve. The only other option would be Colour Change, which is beyond useless as everyone easily finds ways to make it so we have a Super Effective move against it. Such as Ice then Fire.
Finally, we are not making a sweeper or revenge killer, even if said Pkmn would be restricted to being useful against a particular threat. If you honestly want another Pokemon capable of ripping up the opposing team, use something that's already powerful that you aren't already runnning, such as CB Bullet Punch Scizor or LO Collosoil. Utility Counter suggests stopping another Pkmn in its tracks, allowing us to force it to switch or just simply fail to damage. Yes, it needs some offensive capability as we don't want another Shuckle, but we don't want a Sweeper disguised by the name of Utility Counter. For example, picking up on what Izzetmaster said, a Salamence Counter will likely have an Ice Move, an Electric Move and a Rock Move. Which is high type coverage. Combining that with high Atk/ SpAtk would be creating another sweeper.