I am leaning towards investing so that I can pay back my debt faster than I would otherwise and be able to increase my income. 

You will either have to hire and fire successive agents (shotgun approach) or you will have to study and evaluate an individual for some time to see if what others have told you is true (Sniper approach) sorry there isn't a faster way really outside of a lucky pick. 

I would also like to flip houses in between acquiring properties, using the profits to pay off properties faster.

@Cori Sachais see if you can come to an agreement with them. i think a lot would want some kind of compensation for their time but some of them might not find it worth a couple bucks here and there so coming to an agreement such as them being your #1 referred to agent or making sure to use them on any of your on market transactions is appealing. i know i love referrals and loyal customers, it fuels our business!

Until recently, we didn't have the money or sweat-equity time to buy faster.

I pick and choose my deals.1) Find a Great domain name2) Head over to Investor Carrot and get the middle package3) Go through their SEO training which serves as a great little starter on SEO.4) Make your website credible first and foremost.5) When you have a decent credibility score, work in all you learn on SEO6) While you constantly improve your website, start learning about PPC/DMM7) Send out your first campaigns.8) You get your first paycheck9) Dump 90% of said paycheck into your business, by increasing your marketing budget10) Repeat process while ALWAYS working on SEO11) Withing 3 to 4 months (if you get to be as good as SEO as I am) you WILL rank #112) Leads magically start pouring in faster than you can open them in your inbox13) (Optional) Quit paying a cent on Marketing, and enjoy actually investing!

Prior to selling, the property tax and insurance had gone up significantly faster than the rents. 

The rent from that will help you save your down payment faster.

PS pay the contractor in 2 payments on a anything under 2 months 3 payments on anything above 2 months, they will work faster to get to that next payment on long jobs. 

The more you know, the faster you can recognize opportunity.