if beta is low, vbe is higher. when you add a fixed ptat voltage, the total bandgap voltage is higher. there is no trick i know of to compensate for varying vbe (ie varying beta), or else we wouldn't need to trim any of our bandgaps!
so you can consider trimming the gain resistors, or you can investigate whether 70mV of Vbe is really likely - it may be the WC corner, but a fab would have to be in pretty sorry shape to actually give that kind of variation. BTW - what is the beta on that corner? 50 with a typical of 200? my calculations say that 70mv is quite pessimistic in a case like this.
70mV is about 6%. a good figure of merit is about 3% for a quality bandgap, pre-trim. (37mV) but if you're using a standard cell (brokaw, etc) it's just fab variation, and has little to do with your circuit, assuming you know what you're doing and the cell has no boobytraps. i just ran my most recent bandgap from beta of 50 to 250 and it came up as 34mV variation. but on one single wafer we saw 0.6% (7mV) variation, and widest spread from highest lot ever to lowest was about 1.5%.
soooooo - we have to consider whether a beta variation from 50 to 250 is reasonable, or does it mean the fab is allowed to be out of control while they still make you pay for your wafers? if it were me, and we got a lot 6% low, i would send the wafer back and find a fab that can control their diffusions. just me though!