I agree it's very hard to speculate and get close to numbers, but I don't think the growth needs to be exceptional to see a large increase in cap for 13/14.
A 5m increase on 65m is more than a 7.5% jump in revenues. Forget 57% vs. 50% for a second, if the NHL was consistently growing by that much the next HRR determined cap is gonna be quite high. The 11/12 season had a 70.2m cap based on 57% of HRR. If we go conservative on the growth at half that (let's do 4% 'cause it's easier), then the cap for 12/13 would've been 73 for the lockout season, 76m for this season, and 79m for the 13/14 season (I rounded off a lot). Those are far less than the 5m increases you referenced, and we're still talking under the old system. If that 79m is re-adjusted to the current split of HRR (just divide by 57 and multiply by 50) and you're up to about 69.3m. If you did it with 7.5% increases (the 5m guesstimate) and readjusted for the new split, it'd be 76.5m.
The lockout and this year's arbitrarily defined numbers cloud the issue, but if the league grew during these years, then even with the new split, 3 years of growth against the 57/50 decrease could more than balance out.
That being said, did they change how HRR is calculated? Did they alter what is included in HRR(part and parcel of the first, but a little different)? Did they alter how the floor and cap are calculated in relation to HRR? How did the lockout affect growth for the league?
If during the lockout, the shortened season, and the upcoming one the league grew even half as much as it did perennially between the last lockouts, then a 70+ cap for 13/14 is not at all hard to fathom.
My math was back of a bar napkin bad I know, but there's no point getting detailed when it's this sketchy.