Longer bottom times really aren't a function of the overfill or tank type, but rather tank capacity and breathing rate.
A HP 80 and an aluminum 80 hold the same amount of air (okay, yeah, one holds 80 and the other holds 77.2 or something like that but for arguments sake let's say 80 for both.) If you breathe each tank the same, they'll last the same amount of time. Since the HP 80 is at 3500-ish and the aluminum 80 is at 3000, the HP 80 will lose pressure faster (HP 80 is 43.75 psi per cuft while the alum is 37.5). Still, though, you get the same amount of gas from each, 80 cuft. The benefits derived from the HP 80 are the buoyancy and the size. The HP tank is much smaller than the alum, and some people like that. But, in the end, there is no breathing air difference between the two, hence no change in bottom time (based purely on air consumption.)
In overfilled LP and HP tanks, you need to look at the capacities of those tanks. An LP 85 overfilled to 3000 psi gives you a not-so-LP 96. An HP 80 overfilled to 4000 psi gives you a bit-more-than-HP 92. So, for these two tanks and pressures, the overfilled LP 85 would give you more bottom time (all based on ideal gas laws. I'm not up for the real gas law math today, and it doesn't change it by that much.)
Conversely, an LP 66 pressed up to 2800 psi gives you an MP (if you will) 70, whereas an E7-65 pressed up to 3800 gives you an WHP (that'd be Way High Pressure) 75. In this case, the HP gives you more bottom time.
These calcs are based on 3442 HP pressure, 2640 LP pressure, nominal rated capacities, and ideal isothermic gas laws. In reality, many things will affect your bottom time, and the benefits different tanks give with regards to buoyancy and size (read drag and trim) can immensely affect your bottom time. In other words, if you want to improve your bottom time, work on your comfort in the water and trim more than your overfilling techniques.
As an example, if you take your SAC from a 1.0 to a .7 (not extrememly hard to do), you increase your bottom time by 142%. This is the equivalent of turning your HP 80 into a HP 114 with regards to bottom time (in other words you'd need 114 cuft of gas to stay down as long at SAC=1.0 as you could on 80 cuft with SAC=0.7)
To get the 114 cuft in an HP 80 would require an overfill to 4900 psi.
Hope this helps.