It may not have Fire as the secondary damage type, but the Mine Launcher does go some distance to fulfilling this role. 1 direct hit from a Lochnagar mine does ~420 damage to armour, enough to 1-shot the armour of a Spire/Goldfish. If the mine does arm then the damage done to armour is just over 600, enough to break the armour of a Mobula or leave a Pyra with less than armour left. And you can't get much more brawly than a Loch mine
The reload time is very short (4 seconds) but including the rebuild time from Loch breaking the gun (I don't have the exact numbers, it adds several seconds though) you have the extended reload time.
The direct hit damage from Loch is similar to what you were going for with it, but it does lack the second shot per clip. However, the armed mine does give that extra damage boost.
Using the mine without Lochnagar, with only direct hits the most DPS you can get out is (unsurprisingly) with Charged rounds, ~240 damage/shot at 1 shot every 4s, so ~60DPS including reload. This is comparable to the Hades (66DPS to armour with normal ammo, 57 with Lesmok, both including reload and assuming 100% accuracy), so the piercing from the gun can be used in other ways too.
There are a couple of issues with this of course, the arming distance of Charged is 165m, and Loch is 66m, so to make use of direct damage primarily your ship must be closer and therefore be risking hitting any missed, opened mines. While the mine arcs are large (60 horizontal, 45 up, 15 down, also drop to take into account) the turning speed of the gun isn't too great, but it's not too low for most engagements.
It might not be a new gun but there are still ways to get that high immediate damage in brawling situations with what's currently in the game. A new light gun like that would certainly be interesting though.