I think the deductible floor is pretty simple. Your deductible shouldn't be any lower than the average you have in your HSA. Hopefully you can increase the balance of your HSA every year, and over time increase your deductible to match.
For me personally I have a high deductible plan at around $7000 (I have three young kids also), and I have about $6,000 in my HSA right now (since I just paid a huge chunk for braces). I'm very comfortable with that, it will be back up around $10,000 by the end of the year.
If your HSA is just starting to build up you might want to stick with $4000, but if you expect your HSA to reach anything close to $10,000 by the end of the year, and you are able to cover emergencies with other liquidity, then I'd think going up to $10,000 would make a lot of sense. Just make sure you have your HSA contributions at the max so you can build that up for covering increasingly higher deductibles over time.