Your BC 3070RE has a GVWR of 14,000 and probably has around 3,000 lbs sitting on each wheel (maybe a bit less), but because weight is not evenly distributed, you might have significantly more on one or two wheels. Absent individual wheel weights, let's assume 3,300 lbs on at least one.
Looking at the Goodyear inflation chart, 80 psi would support 3,042 lbs. To get to 3,300 lbs, you'd want 90 psi. If you add a bit of safety margin, you might go up to 100 psi and a carrying capacity of 3,550 lbs per wheel.
If you can get individual wheel weights, you'll have a better idea of where you need to be. In the meantime, I'd suggest 100 psi and keep and eye out for abnormal tire wear.
Can you use the Goodyear chart with confidence on a Sailun tire? I don't think the construction is quite the same. Goodyear uses steel from bead to bead whereas the Sailun documents don't claim that. But I think that's for protection against curb hits, not for carrying capacity. Nevertheless, the max 110 psi weight rating of the Sailun is the same at the Goodyear G614. It seems reasonable that you could assume the carrying capacity at lower inflation levels is similar.