Brompton owners

Right, I've got a recurring issue that's bothering with me on my S6L with the derailleur shifter.

Some time back I got rid of the stock (pre-2017) 2s shifter as it kept shifting when I went over something rough, and am running a remote lockout switch instead. It's been fine, mostly.

However, the last time I self-serviced or cleaned my bike (or might have just fixed a puncture) I noticed that shifting into the big sprocket was a struggle. Everything seemed fine - the dog-leg wasn't overly tight and the cable was new and moving freely. I just had to tighten the chain tensioner as it was a bit lose - problem solved.

I'm in that same scenario again after cleaning my bike. Yet I've made sure not to make the same mistake of having play in my chain tensioner. Shifting into the lower cog is worse than it's ever been. Two things I've noticed though:

1. If I add cable tension at the barrel adjuster, shifting improves, but the adjuster is out quite considerably, so I'm considering getting new cables as I'm due anyway.
   
2. The only thing that I've change is to revert back to my 13t/16t cassette, which isn't badly worn but did see more usage than newer 12t/16t that was sold to me buy mistake and has been on the bike. I much prefer the slightly lower gearing though.
   
   

Any tips before I take a look at this again tonight? I'm gonna inspect and maybe swap the inner gear cable or just add tension on the existing one, but not at the barrel adjuster this time.