You could also overcome it with a two-way directional control valve such as Clippard's MJVO-2. You could have your trigger depress the pin on the directional control valve right before the pin is pulled. That might be difficult to do though, so you could also just attach the valve directly to your trigger so that when your finger squeezes the trigger, the pin plunger on the trigger is depressed first, cutting off the live air hose to your tank, and then when the trigger starts moving backwards, it pulls the pin in your tank.
A pin pull tank would give you the most volume and range (like a early gen BBBB or beserker ~100'-120') but you would be bleeding your reserve tank out your barrel as long as the pin remained pulled. You could overcome that with a quick trigger pull, but that may require more thought than you would like to invest while in battle.
Now that we are talking about valves, the MJVO-3 has a much higher flow rate than the MAVO-3 does, so I suggest using that. The MAVO-3 may be too small for our requirements, and the MJVO-3 only costs a few dollars more anyway.
A back pressure tank would give you ~ 70'-90' & require a clippard MAVO-3 valve (buy from ebay not clippard. Clippard shipping costs are brutal)to isolate the reserve tank and fire your primary.