But what would the ship be which could take down a panzerschiffe...
Stopping a raider and sinking it aren't necessarily the same thing. You don't actually need a better ship to stop it raiding a convoy, you just need one the panzerschiffe can't risk engaging. Old battleships saw a lot of WWII use for distant escorts of convoys where there was a raider risk, they might be too slow for battle-line use, but they could sink a raider, or cause enough damage it wouldn't be able to evade a hunting force. OTOH they couldn't pin down the raider if it saw them and decided discretion was the batter part of valour. Smaller units might not have had exactly the same threat value towards the raider, but RN policy was that the escort would head straight for the raider, guns blazing, in the hope that at best they would land a lucky shot, and at worst they would give the convoy the chance to scatter behind them. Sometimes the escort lost, such as with Jervis Bay vs Admiral Scheer, but sometimes the escort won, as with Bengal and Ondina vs Hokoku Maru and Aikoku Maru.
There's a subtle difference between the design requirements trade protection role and the raider-hunter role. The trade protection cruiser just needs to be enough of a threat to make the raider think twice about engaging, so strategic endurance and moderate firepower drive the design, but the raider-hunter needs to be able to force the engagement and win it. Which means it needs tactical speed and significant firepower. The RN built the Hawkins class as raider-hunters and they ended up far larger than existing cruisers (excepting the ACRs, which are really second class battleships), and too costly to build enough of them to be effective as trade protection cruisers. The Admiralty eventually came to see the Hawkins as a mistake at every level, because they drove foreign cruiser design towards 8", 10,000t 'Treaty Cruisers', whereas a 6", 6,000t trade protection design fitted much better with RN trade-protection requirements. Stopping that kind of tactical success, strategic failure was why the Admiralty's 'Future Building Committee' was so influential.
It's telling that the WWII solution to raiders wasn't some modernised Hawkins-equivalent cruiser, but a system of nodal reaction forces, such as Force H, ideally built around a battlecruiser or an aircraft carrier, or with several cruisers operating together as a second-best, as was seen when Exeter, Ajax and Achilles ran down Graf Spee. That's why the French response to the Panzerschiffe was to build the Dunkerque class, and it was probably at least part of the drivers in the Alaska class.