Ignoring debates about what constitutes the "Goldilocks zone", the issue of the Earth-Sun (AU) distance change is not terribly settled either.
Howard appears to be using data from a somewhat cited 2004 paper by Krasinsky & Brumberg, who estimated 15 ± 4 cm / year. (There were other papers around that time that found comparable figures, using similar methods, e.g. 7 ± 2 cm/year.) However, some years later (2012), other researchers (Pitjeva & Pitjev) from the same (Russian) institute have cast doubt on that Krasinsky & Brumberg figure and its method of estimation. According to the latter, the margin of error is greater than the estimate, i.e. 1.2 ± 3.2 cm / year.
As far as I can tell the 1.5 cm figure given by another astrophysicist in Forbes, which is cited as the true figure in the self-answer, originates from a pretty simple model (that is probably not publishable as such in a peer-reviewed venue, nowadays), and lacks an estimate for the error margin.
More on this at https://astronomy.stackexchange.com/questions/49979/is-there-something-close-to-a-consensus-on-earth-sun-annual-distance-increase-s
Even if we grant the 0.15 m/year drift, rounding AU to 150 million km = 0.15 x 10^12 m, i.e. 0.15 trillion meters, means that the Earth-Sun distance would increase by one trillionth in a year, or it would take a trillion years for the distance to double.
But Mars sits at about 1.5 AUs. So to get that kind of increase (50%) it would take half a trillion years, not half a billion. I suspect Howard made this off-by-a-factor-of-1,000 error in his calculation.
This constant speed model, however, is pretty bad, because it ignores a bunch of things, like the accelerated rate at which the Sun will shed mass as it expands to the red giant stage. Wikipedia cites one 2008 paper, according to which the Earth-Sun distance will reach that 1.5 AUs much sooner, but the habitable zone (HZ) will also have moved outwards much faster...
Certainly, with the 10% increase of solar luminosity over
the next 1 Gy [...], it is clear that Earth
will come to leave the HZ already in about a billion years
time, since the inner (hot side) boundary will then cross
1 AU. By the time the Sun comes to leave the main se-
quence, around an age of 10 Gy (Table 1), our simple model
predicts that the HZ will have moved out to the range 1.29
to 1.86 AU. The Sun will have lost very little mass by that
time, so the Earth’s orbital radius will still be about 1 AU –
left far behind by the HZ, which will instead be enveloping
the orbit of Mars.
By the time the Sun reaches the tip of the RGB, at
12.17 Gy, the Earth’s orbital radius will only have expanded
to at most 1.5 AU, but the habitable zone will have a range
of 49.4 to 71.4 AU, reaching well into the Kuiper Belt!
I can't say how much consensus that paper has (beyond the fact that the Sun will move to red giant stage), but it shows that such things aren't simple to calculate. (The paper uses the NASA-like def of habitability "conditions on it allow the presence of liquid water on its surface".)