@Chris Meunier - to clarify my math below, I'm assuming you're making $600 per month right now which comes out to $7200 / year. I wasn't sure whether to use that or $500 per month which would come out to your originally-stated $6000 per year, so I just picked one.
I'm also assuming that you're taking into account percentage expenses such as CapEx, maintenance savings, vacancy savings (I did see him mention "before any maintenance costs", @Dan H.)
The last thing that I will assume is that you're sitting at exactly 20% equity on a loan of $262,500 - the reason for this is that it'll take out any extra equity that you could possibly pull out of the current property. It also gives me the assumption that you have $52,500 currently invested.
Following these assumptions:
$52,500 - total invested currently
$7200 - total annual income
$210,000 - total available cash
Option 1: put all $210,000 into your first property
$262,500 - total invested currently
$30,000 - total annual income
$0 - total available cash
In another 7 years, you could double your income to $60,000 if you save all of your rental income to reinvest. I'm going to assume that you won't leverage this property by refinancing or taking out a HELOC since you went through all of the trouble to pay off the debt in the first place.
Option 2: put all $210,000 into 4 more properties with similar cash flow as your first property (this comes out to exactly $52,500 * 4 = $210,000)
$262,500 - total invested currently
$36,000 - total annual income ($7200 * 5 properties)
$0 - total available cash
In another 5.8 years, you could double your income to $72,000 if you save all of your rental income to reinvest. If you leverage your 5 properties and refinance or HELOC, you could do this sooner.
The numbers above are snapshots of what you will have immediately. Cash flow is higher in option #2, at the cost of increased debt. Assuming fixed interest rates, this shouldn't bother you unless if you want to do speculative investing (will your properties appreciate or depreciate?)
I want both of my points to stand out, so I was liberal with my use of bold.
When investing in real estate, debt shouldn't bother you as long as it increases your cash flow. If you believe this, then Option 2 should be the logical conclusion. Smart investments, and allowing for proper vacancy savings etc will protect you from any "all-nighters trying to get a tenant because the mortgage is coming due". If you need to pull an all-nighter, and if you don't have one month of mortgage saved up in vacancy savings, you've been failing in your investments.
If your goal is to increase passive income in order to retire, then Option 2 will get you there fastest. Option 1 will still get you there, but it will be slower. You have to look at your own goals and decide how quickly you want to get there.
A long read - sorry for that. I wanted to at least give some maths to back my answer.