A fellow pilot asked me if I had the time to regain the sec-status of his PvP toon for a generous reward. He had real-life commitments happening and didn't have any spare time. I agreed and, after a few pointers on the best way to do this, I got to work.
Had I known the level of time required, perhaps I would have declined the favour.
OK, so the best way to increase standing for a character at the back end of -10 is relatively simple. Ratting. A speed-tanking Manticore was the ship of choice and I headed to a 0.1 system where the NPC Battleships live. Taking out NPC BS's is the way to do it, as these have a significant standing increase over any other NPC pirate ship out there. At first, I picked a solar system and began 'grooming' the belts. If you warp into an asteroid belt and a spawn containing a Battleship arrives, just kill the BS and leave his buddies alone. After about 20 minutes, the BS will reappear. If you warp to a belt and there is no BS present, kill the entire spawn and hope that the next group will contain the precious BS. If it doesn't, wipe out that spawn and repeat until you get the BS.
You can do this until all the belts with spawns (note that only a certain percentage of the belts will ever get spawns at all) and then you can just warp from belt-to-belt wiping out the BS's. This is a great way to earn ISK but, as I found out later on, not the best way to gain sec-status. It wasn't until I posted my frustration on Twitter that @DavidKMagnus pointed out to me that you will only ever get ONE sec-status increase PER SYSTEM every 15 minutes. This means that whatever ship you kill first in the belt will be your status increase for that 15 minutes window. From my experience, a BS will give you up to a 0.2 sec-status increase while a frigate might only give you 0.02. So if you spend the best part of the day in one system and happen to kill a Frigate as each 15-minute timer runs out, it will be a while before you see any credible gain. For the few days previous to the welcomed advice, I wondered why my sec status increase was going up so slowly after killing many 0.17 - 0.2 BS's. This fifteen-minute timer was the reason. But this timer only exists within the system, and jumping to a new system will start it's own seperate timer.
So the best method involves the need to travel from system-to-sytem killing just a single BS before proceeding through the next gate. I was lucky enough to find a loop of 0.1 systems not far from where I was operating at the time. I jumped to the first system of the loop and warped to asteroid belts until I found one with a BS, made a note of the belt and system and then proceeded to the next. I did this until I arrived back at the start of the loop. Then I put the Manti to work, killing the BS in the noted belt before jumping through to the next. Then the next, then the next. By the time I got back around to the beginning, the 15 minute system and 20 minute spawn timers were just about reset and so I went around again. And again. And again. I did this until the sec status was where it needed to be. Using this method, the status rocketed up in comparison to my original technique.
By the end, I was a zombie and fed up of NPC rats. It has deterred me from ever getting my sec-status below -1.99 on any of my toons. And spending so much time permanently in Low-Sec made me value HS so much more from the simple reasons of aquiring equipment and ammo. This is a lot more challenging in LS for many reasons - gate camps and the sheer sparsness of sell-orders in Low-Sec (in the area I was operating in, anyway).
So there it is - a quick run-down of how to regain your sec-status. If you ever need to do it, make sure you have a good supply of coffee.