I believe those double sided deadbolts aren't legally allowed in residential homes, you may want to check with your local laws. In case of fire it could potentially trap people inside. Medeco makes a set that has a removable keyed knob (basically a key that has a knob attached), but that's pretty much the same as just leaving a key in the door. And unless everyone in your family is disciplined, that's what will eventually happen anyway, they'll just leave a key in the lock for convienence

The longer screws might work, but if the wood itself is weak it won't help much, it'll still rip out of the frame. There's a reinforcement strip about 3-4 feet long that screws onto the frame and spread the load over a much larger area, it's called strikemaster or something like that. You don't have to do much modification either, it's just a very long strip of metal that replaces the strike plate.

You'd be surprised how easy it is to break into a gun cabinet. Whatever it is just make sure to bolt it down, because if they can carry it off, it doesn't matter how secure it is. One motivated person can easily carry off a 300 lb safe.

You can also look into installing home security cameras. I just installed a system not too long ago, it isn't very hard. It won't physically stop anyone from coming on to your property, but it does give you a sense of security to be able to watch your house when you're gone. I'm halfway around the world right now and I can see what time the mailman arrived today and anyone that came onto the property.