My lender is saying that they go off of the lower of the two scores, and it must be at least 720 to qualify for only 15% down. 

not really...regardless you need a lower purchase price to make either option work. 

Hey guys,I found a property with a special situation: it has two lots - one lower lot with a house and one upper lot that is empty.

I am simply pointing out that it is very RARE for a great exit to line up with a great acquisition in the time frame allotted for in a 1031. 

I explain to the prospective tenants that in exchange for lower rents I expect tenants to adhere to maintenance rules such as yearly carpet cleaning, monthly house cleaning, AC filter changes etc.

But I was wondering if more experienced investors would recommend trying to get it rented sooner, especially before the school year started, by lowering the rent?

Typically a lower yield property is the market determining that that property is lower risk than some huge pro forma cash flow property, which likely has that proforma cash flow being so much larger because the market views it as a higher risk asset.

You will typically receive lower rates than what you would see with a hard money lender. 

Would it be better to go for a lower end home and use a 203k loan to rehab and finance or get one that's not as bad off and start there?

Much lower price point for ours than yours and they aren’t lasting on the market.