From your description, you have 134k in equity controlling 330k of home value and producing $1,300/month in rent.

I'm finding a lot of places that can produce a small amount of positive cash flow but none of these places offer good opportunities to refinance in a few years.

From the day your sale closes you have 45 days to produce a list of potential properties. 

If I buy one more house it will be my last slot, so I was hoping to consolidate.

My bank will give me some credit from my other income producing properties, but it isn't enough to qualify me.

Doug Llewellyn (People's Court) was the producer behind the show and thought it was going to be his HUGE money maker!  

From my understanding if you have no intentions of making your primary residence into a income producing rental for at least 12 months the 1031 will not apply.

I challenge you to find the Midwest city that has produced a better ROI than the worst coastal Cal city for any of durations listed. 

If your plan involves continuing in real estate investing and you wanted to sell so you could buy a better producing piece of investment real estate then the 1031 would accomplish the same thing. 

@Manny S. - lots of people will want to sell you.