You hire a collection agency.
Court judgments are also reported to the credit bureaus and will screw up your credit worse than a late payment to someone. The credit bureaus call them “public records,” because they are matters of public record.
Yes, but only for as much as it is worth. Which may be very little. See above.
And the whoosh just keeps on going and going and going…
Grand, ain’t it? 
Actually, I do not accept checks from new clients. Once they are established, I accept checks. Our policy is to allow 72 hours for a bad check to be made good. If not, the account is sent to a collection agency and to the county’s DA’s bad check program.
For large checks, I call the bank and ask if the check will clear. The banks cooperate, although I do not know if that is a general policy.
There’s lots of things you can do to enforce a judgment.
(This is in England & Wales, but I imagine the principles at least are similar in most common law countries)
Execution
Property of the debtor (except ‘tools of the trade’ and essential items) can be seized by a court enforcement officer/bailiff and sold at auction.
But - Goods rarely realise their true value at auction; the bailiffs can’t just break into people’s property and take things; the bailiff’s costs are deducted from the proceeds of sale and it only applies to tangible and movable assets - no land, no bank accounts.
Third Party Debt Order
Say your debtor is owed money by someone else, or has a bank account in credit. You can get a court order requiring the third party to pay the money directly to you. It’s good because you sidestep the deadbeat who’s refusing to pay and deal with someone else.
But - It’s expensive - you’ll need at least two court applications and you’ll be responsible for the third party’s costs as well as yours; if there’s other unsecured creditors the court will probably refuse; if it’s a joint account the court will refuse; you need really accurate and up-to-date details of your debtor’s account and if the court isn’t convinced there’s going to be enough to pay off the debt, it won’t make an order.
Charging Order
Gives you security over your debtor’s land. Obviously this doesn’t give you money right away, but it does get you some security at least. Once you’ve got the order you can apply to court again to order the sale of the property.
But - It’s expensive for most of the same reasons as a Third Party Debt Order, only this time there’s at least 3 hearings; it doesn’t really work if the property is jointly owned; the court is unlikely to order a sale if the property is a family home.
Attachment of Earnings
Gets your debtor’s employer to pay money from his salary direct to you. This isn’t very expensive, is out of the hands of your debtor and is pretty embarrassing for them, as their employer knows.
But - It’s slow, as you’re paid by instalments; it only works if your debtor is an employed individual (not a company, self-employed or unemployed); you need to know the details of where your debtor works; if the guy keeps changing jobs then it becomes hard to enforce.
Finally, if all that fails, you could try:
Insolvency Proceedings
Apply to make your debtor bankrupt. This puts a lot of pressure on them and if they’re a sole trader can cause them huge problems.
But - You have no priority as the petitioning creditor - you line up with all the other unsecured creditors; it’s expensive to bring insolvency proceedings; if your debtor hasn’t got much money and/or lots of people with priority over you then there’s a fair chance you’ll get a tiny proportion of what you’re owed, or nothing at all.
So, there’s lots of things you can do to claim your money but you’ve gotta decide how much time and money you’re going to spend trying to get it.
How to avoid paying an $8,700,000 lawsuit!
That seems like a very sound policy. Unfortunately, it’s not completely without risk. Hopefully the good will from and convenience to your clients is worth the occasional loss.