Do I need to improve the property/raise rents enough over the course of the 2 years that a bank will give me a traditional loan at that point?

I would hit up you local banks, S and Ls.

Recent Bigger Pockets episode motivated me to reach out to US Bank about their mortgages and loan products. 

Did you get a bank loan for this? 

@John Beck your best bet is to start with local banks and credit unions who know and understand the area. 

Account Closed i don't trust anything when it comes to sellers and brokers.you need to verify as much as you can. with rent roll, you want to make sure that you know what rents are currently paid, not just Physical occupancy But also Economic occupancy - that means tenants that actually paying rents. you can verify these by asking for bank statements, and schedule 1from the TAX Return. 

Do I pay it out of my LLC's bank account or continue paying out of my personal account.

I would like to pay off the arrears and get some favorable rates from the banks and get to rehabbing the properties right away!

Nothing against them, I use NFCU as my personal bank of choice, they are just not the best at VA Home Loans IMHO - https://loans.usnews.com/va-loans 

Others are banking on the market being hotter than the cashflow and therefore wanting in because they think appreciation is their investment method of choice.