Balancing a bullpup

I got a crazy idea and wondering if anyone has gone down the same path. I love bull pups and my taipan is incredibly accurate. However being a bullpup it is rear heavy, which is great for shooting offhand but when shooting out a window or off a bipod the rear of the rifle must be supported or it will want to tip backwards. I’ve grown accustomed to this and always put some downward pressure at the front of rifle and support the back with my hand.

I’m trying to add enough weight to the front of the taipan that way it can balance on a shooting bag when I shoot out my window, car or bench. So far I’ve attached a arca camera plate to the stock and attached a 1lb Ingot of copper to the plate. The balance is much better but not quite there. I still need room for my hand to be on the grip/trigger. Trying to brainstorm to think of more ways I can add weight. I really didn’t want to add a bipod hanging on the front but maybe that is the best option. I much prefer to shoot off a bag now.

Anyone else try something similar? Am I just crazy? Please mind the stock of the gun, it is in between paint jobs lol. This is my project stock.
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You can route out the inside of the front part of the stock and fill with lead shot or tungsten powder then epoxy over the top to keep it in place. That way it would be hidden and no extra parts hanging off taking up support hand space. Kind of a permanent solution though and makes a slighty heavy gun heavier for woods walking and shooting off hand.
 
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How about going the opposite route, and remove some of that wood from the rear to balance it out? Noticing that you do paint jobs and the like to it anyway, it wouldn't be hard for you to remove that two-by-four of lumber sitting inside of that recessed area. With a hack saw blade, file and some sanding, it looks like that would help to balance it out pretty nice. Then you wouldn't have to add as much weight to the front, if any...
 
I could and have used a rear bag before but when shooting out my window or car the rear bag would not work. And neither would a bipod.
I know I mentioned bench, probably shouldn’t have. This is more about shooting from positions where rear support is not possible. I guess im trying to turn the taipan into some type of PRS air rifle. lol.

Gun is tuned for a 18gr at 900fps. It has a LW barrel. Barrel is polished and the barrel crown cleaned up by motorhead.

I like the idea of removing wood from the rear. That might be the best solution. I have 2 other taipan stocks so I’m not afraid to try that.
 
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