I is easier to remove the engine from a bugeye than it is to remove and replace the bonnet. So why risk damaging the bonnet by trying to remove and replace it?
Remove the carbs & intake as one unit, keeping the cables still connected if they will go back as is and set them on the master cylinder.
Remove the distributor, starter, and sometimes the oil filter if yours is one that sticks out with the angle adapter.
Undo the bellhousing bolts, use a block of wood under the oil pan and a floor jack to raise the engine some, pull the jack forward some, raise it to clear the steering rack.
Place a towel over the steering rack, slide the engine onto the rack.
If you have a helper, get him now, have him balance the engine on the rack while you scoot the floor jack out from under the car and position it in front of the car. Now slide the engine onto the floor jack.
It fits between the radiator supports with the exception of some oil filter adapter spacers.
If you do not have a helper, you can balance the engine with one hand on the rack while you maneuver the jack with the other hand.
It is not 1/2 as hard as it sounds. I do it all the time with 3 Bugeyes in the family, most of the time by myself with the balancing act.