You can't fix stupid - but you can muffle the noise with duct tape!

Anyway, low and behold 6 days later the tenant messages me to tell me the unit is power surging or something because the lights in the house were flickering and it was making a loud noise outside. 

Thick, high quality noise barrier foam was laid down (beware the cheap stuff) and then tile installed on top of it.

What is your suggestion on the noise complaint?

The plan was to not only create a nice tax shelter but to also create some cash flow so I didn't have to grind so hard.

My question is: Am I going to be able to charge the average for my area or will I have to lower it because of the proximity to the railroad noise?

I can appreciate you want to do as much of the work as you can but just know that people won't want to live with construction noise. 

Run the A/C for the entire house and charge the renter the difference.Central A/C is probably more efficient and quieter, so it's probably not going to cost your tenant any more than the window units did and should be of better value due to the lower noise level and better cooling throughout.

Another month goes by and I get complaints from the downstairs tenants about high levels of noise in the early morning, issues in the laundry room, and constant badgering via text for the upstairs tenants.  

Time is most definitely on your side though so just keep grinding and saving money until you can afford a down payment on a real asset.