You can leverage retirement accounts or credit cards amongst various other tools. 

You own 3 sfh 4K should be change to you Its probably change to someone who uses leverage or other peoples money.

We have all lived in a very comfortable environment of low-interest rates and quantitative easing/easy money policies for a number of years, and this has benefitted both home owners and ordinary real estate investors with low leverage costs.

I generally reassess every couple of years and either leverage my business relationships or dump them.

Yes you are entitled to more but they are just scared your over leveraging with 2 homes.

@Ryan Tuleja This could be a number of reasons1) Is there a large influx of "like kind" properties available in your area2) It could be over priced for "like kind" properties3) Your analysis could be slightly off, build your team and leverage their knowledge of the area (find a real estate agent who invests in the same area) You may be working your numbers with a lower profitability than local investorsI suggest finding a local RE investor meetup or group.

I would like to leverage equity in paid off investment properties in Texas to acquire more properties. 

You could find a partner that will inject cash for a piece of the cash flow and equity kicker. 100% leverage is tough.

I'm exploring options of getting into investing without cash out of pocket, but also plan to use our equity post-addition as a way to leverage into my first property if I haven't done so yet.

However if you buy a bigger nice 2-4 unit, or leverage that into a 5+ unit building and live in it the whole time than you may not need to do the 1031.