You can look at this calculator to give you a rough idea of what you could have got with your priming
Calculate precisely how much priming sugar to add at bottling time (bottle priming) for your home brewed beer. Works with a variety of priming sugars.
www.brewersfriend.com
and this for general carbonation related to temperature.
Beer Carbonation Calculator
There is a formula for working out how much CO2 is needed in weight per unit of volume but I don't know where to find it.
This would tell you how many bulbs are needed to force carbonate a barrel. Trouble is to force carbonate quickly you need cold and high pressure
not sure that either of these possible with your shed and bulbs.
It's all about balance.
Also always suspect a leak with a PB until proven otherwise.
Note you did prime the PB with the 80g of sugar plus a bit of boost carbonation with the first bulb.
I suspect when you work it out it's a bit overcarbed and hence impossible to dispense without throth. Can you chill the barrel down? Milk bottles with water from freezer and then insulate it to keep the cold in. That will help.
Trouble is it's going to be hit and miss without a pressure gauge.