Low pressure with shallow sand point, increased pressure tank to 86 gallon, how do I use more of the water in the tank before the pump turns on?
Water storage in a pressure tank is a function of what pressures it swings between as well as size. The most storage for a "common" setting is at "20PSI on / 40PSI off" - for the usual pressure switch that has a fixed 20 PSI differential, water storage reduces as you move to 30/50, 40/60, 50/70. A setting lower than 20/40 is not normally used. One 86 gallon tank I'm looking at has a capacity of 31.8 gallons liquid at 20/40, which shrinks to 23.2 at 40/60. The 20 gallon tank in the same series is 7.4 and 5.4 gallons at the same pressures, so something is clearly wrong with your installation if you have no increase in capacity.

Since you mention better pressure, I see one of two possibilites - 


You (or a plumber) altered your pressure switch setting as well as changing the tank.
You bought a tank that was pre-charged to a pressure above your lower working pressure and did not adjust it when installing on your system.


In the latter case, the tank stores essentially no water below the pre-charge pressure, so it will run out and pressure will drop precipitously - but what water is stored will be at a higher pressure. This would match up with your perception that the pressure drops as the pump kicks on.

To resolve - Set your pressure switch to 20 on, 40 off, assuming it is the typical 20PSI differential, adjustable setpoint switch. Turn the pump breaker off when adjusting the switch, as the mechanical and electrical parts are often under the same cover.

With the system turned off and water drained, set the air pressure on the tank to 18 PSI (2 PSI below the cut-in, if you decided to change the setting to something other than 20/40.)

Or - simply record what the pressures are when your pump starts and stops - then drain the system and set the pressure tank air pressure to 2 PSI below the start point. It seems unlikely that your pressure switch is so far mal-adjusted that you'd see no capacity increase, so I'm leaning to an over-pressurised tank as the most likely situation for the conditions you describe.

Incidentally, if you have not discarded the 20 gallon tank and it's still in good condition, you can connect it to the system for additional capacity.