Running 315's for steers

315's will help with your capacity for the weight legal side on your steer.
As for the dipping on the rear part, I believe you need to get your 5th wheel farther ahead of your center on your drives.
I run a 265 wheel base and my slider goes center of my lead axle and center axle. I'm running a tridem on the back.

 

If it's a daycab I'd say shorten your frame up tight an roll on..

 

To put some numbers to that "nose-up/light steering feel" what are your axle weights on various loads?
Your fifth undoubtedly is too far behind center of drive tandems. Replacing with 315's "might?" help counter "the effect", but only slightly, as you're not addressing the direct cause by doing so. You need to get more weight transferred over that 14.6k front axle.

 

Start with cutting your frame so you can slide the fithwheel more to the front.
Running wider tires will not help the feeling you decribe.(i have 315's as steer tires and my FEELING is that they work best with a high load on them)
Raising your nose higher will actually reduce weight on your steers and put more weight on your drives,aldough it will be a very small difference between the 2 setups.

 

That pretty much tells the tale right there. In fact,, seen some that when the fifth was set too far back the heavier the load... the lighter the steer weight.
As said before, the 315's will help you max out the steer axle, but imo, I don't think you will get a world of difference, or even close, as far as putting more feel/steering response for the steering.
It's not much different than those old pickups/cars you see when pulling utility trailers with far too much tongue weight. Makes the rear sink and no weight on the towing vehicles front end.

 

Don't cut the frame, what you need is a flip up neck extension for your front jeep. Never cut a good double frame, you'll regret it if you ever want to add a lift axle and you need more space on the frame to get you 14'1" separation to your steer. The 315's are a good idea regardless

Also, check if the jeep has two kingpin positions, and if it does make sure its set to the front most one, that might give you enough separation to slide your fifth wheel up without hitting the jeep