It might help to turn the tables a bit. Below, I have answered each question with a question. Hope it helps.
1. How would a DRO that is lying about weapons purchases and hiding weapons from 3rd party inspectors be stopped from taking over violently?
How would the Executive branch of a government, if it is lying about accruing military power for the protection of the populace, be stopped from violently taking over the country?
2. Couldn't a DRO just lie about the "10 million dollar deal" just long enough to become organized and powerful enough to take over?
Couldn't politicians just lie about their campaign promises just long enough to gain power and take over? (ahem, Nazi Party)
3. What if a DRO grows quite a bit and then a new guy comes in and starts murdering people and tries to start a new state?
What if the legal powers of the government are expanded quite a bit and then a new President or Party comes in and starts imprisoning/murdering people in an attempt to gain a dictatorship?
4. How would competing, individual DRO's fight against a large-scale attack such as nuclear/biological weapons or a large scale invasion from a well-armed nation?
How would separate communities, without a standing army or large tax base, fight against a large-scale invasion from the most powerful military in the world? (Hint: American Revolution) Also, voluntaryist societies can have nuclear/biological weapons too. Keep in mind, there are plenty of historical examples of large, advanced militaries proving unable to take over territories defended by small, guerilla forces.
5. How many people would actually have fears or care enough to be constantly watching the DRO for any suspicious activity (I'll admit it's a cynical question to begin with, but I didn't have an answer)?
How many people would actually have fears or care enough to be constantly watching their government for any suspicious activity or concentrations of power?
6. Wouldn't a DRO be unstoppable if they found just one corrupt bank willing to not seize the DRO's assets?
Wouldn't a state military be unstoppable if they found just one corrupt Congress willing to not withdraw funding?
7. Wouldn't DRO's just turn in to large gangs, fighting each other for power? (I said that people wouldn't fund or support them if they did this, but they then noted that by this time they could just start subjugating the people under their respective contracts)
Wouldn't states just turn into large gangs, fighting each other for world-power? If people revolted, couldn't they just start subjugating them under threat of force?
I think you'll pretty much find that any argument questioning the fragility of the DRO arrangement can be applied just as well, if not better, to statism. I'd rather live in a society that was at risk of coercion (voluntaryism), than one that guarantees it (statism). I understand the concern that a DRO could become a non-"representative," and thus less accountable and more tyrannical state. However, it is false to assume that a certain form of statism (i.e. a republic) is less susceptible to tyranny than a voluntaryist society.