If you are going to ride both paved roads and unpaved trails with it then you will really be limited in range of gearing. You'll either not have a low enough gear for off road. Or you'll not have a high enough gear for paved roads.

Shimano has a bunch of 1x mtb cranks with varying sizes of chain rings if you look on their website. You'll have to match up one that will fit your BB shell. I wouldn't necessarily try to stick to your current BB. You'll limit your choices in cranks too much for what is only a 18 dollar part. Assuming of course your BB shell can handle other bb types like ISIS, Octalink v2, or even 2 piece cranks. SRAM has some too as well as many other crankset mfrs.

So what's been the problem. If your shifting problem isn't on the front, then you'll still have a shifting problem whether 1x or 2x, 3x or no x.