The only two ways to rectify this are (1) purchase the property far below market price or (2) significantly increase the property net income usually through some method of “repositioning”. 

Although you will be unable to combine them for a while unless the place appreciates rapidly.

so would like to start building our portfolio in a State that has consistent appreciation with room for rents to increase going forward."

I made the mistake of letting someone get in one of my first units that was a bit off the 3 times, they were great tenants very kind and enjoyed their stay and experience with me, but could not afford it when I increased the rent on them, which is something you will have to do because of rising insurance/tax costs.5.)

Quote from @Cameron Moore: Exactly. 15 years ago, I noticed an increase in owners using insurance to pay for a replacement roof, usually to sweeten the pot during a sale.

Do the math and you'll see it doesn't make sense.The best way to invest: increase earnings, reduce expenses, and save.

The shorter the prepayment term has an impact on increasing the rate.4.

Assuming you go the HELOC route, another option to reduce your costs assuming you have decent credit is to look at credit card balance transfer promotions.Back in 2003-2004 I had HELOCs on my investment properties and interest rates were increasing.

There are still properties that can increase their rents, and may make for a good investment.  

In 2022 the rents increased 12.1% year over year which was the 3rd highest in the entire country per https://www.axios.com/local/cleveland/2023/02/14/cleveland-rent-prices.