Its no secret the 160 pumps are pretty much uselss past 2,000RPMs.
This is a myth, they are only useless above 2k when they have stock governor springs and accordingly defuel at 2200. It is true that they are "less great" for making power up high due to the reversal-inhibiting cam, but the short plunger fill only starts to become an issue around 3500 rpm and cranking up the supply pressure can overcome a lot of that. I'll be happy to post dyno graphs of my 160 on my new motor once it's broken in. The injection pump will definitely be the limiting factor in producing power, but the odds are in my favor that it'll be the most power ever made with a 160 on this dyno.
Back on topic, tightening the stock governor springs can improve throttle response but will result in a soft idle, making it easier to stall a manual on takeoff.
There is one common brands out there of 3k/4k kits that have a spring pack imbalance which will result in a highly sensitive section of the rev range of 2-300 rpm, located somewhere between 1500 and 2000 rpm, when you install the kit at the recommended preload. Other brands (that I can't vouch for on here due to a potential conflict of interest) don't have this issue when ran as a 4k.
I would agree that actually being able to rev to 4000 rpm is of little use to most towing applications, however, you can run a 4k pack and loosen it to your liking to get the idle firmness and midrange throttle response you're looking for. Running a loose 4k, in my opinion, would be your best play here. Looser/less preload on the packs gives better idle firmness at the expense of throttle response and RPM ceiling. Tighter has the opposite effect. I have my old 3k/4k set (Pac with machined bases) in my pile of dead 5.9 parts I would be happy to send you for the cost of a beer and some postage.
Also, a lot of the complaints I think exist on forums and social media surrounding GSK installs boils down to installer error. It's very easy to get the packs imbalanced, especially if your pump's governor studs aren't flat on top. During my 5.9 build this spring, I went to install an experimental spring pack that should have functioned as a 4500-rpm kit (with the ceiling of a 5k but without the sketchy throttle response common to 5ks installed by home-gamers). When I had it on the truck, during the 5.9's extremely short life, it was doing all kinds of weird stuff. I blamed the packs, but it turned out to be an adjustment imbalance. I've installed dozens of these things and I still managed to mess it up on my own pump. I guess it can happen to anyone.